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Intention-based reciprocity and the hidden costs of control
Journal of Economic Behavior & Organization 92 (2013) 55–65
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Journal of Economic Behavior & Organization journal homepage: www.elsevier.com/locate/jebo
Intention-based reciprocity and the hidden costs of control Ferdinand A. von Siemens a,b,∗ a b
Goethe University Frankfurt, Grueneburgplatz 1, 60323 Frankfurt am Main, Germany CESifo, Poschingerstrasse 5, 81679 Munich, Germany
a r t i c l e
i n f o
Article history: Received 20 November 2012 Received in revised form 23 April 2013 Accepted 23 April 2013 Available online 10 May 2013 JEL classification: A13 C70 D63 D82 L20
a b s t r a c t Empirical research suggests that – despite strengthening conventional incentives to put in effort – exerting control might reduce worker performance. The present paper shows that intention-based reciprocity can explain such hidden costs of control if individuals differ in their propensity for reciprocity and preferences are private information. Not being controlled might then be considered to be kind, because not everybody reciprocates not being controlled with high effort. This argument contrasts existing theoretical wisdom on the hidden costs of control that is almost exclusively based on signaling. © 2013 Elsevier B.V. All rights reserved.
Keywords: Intention-based reciprocity Incomplete information Hidden costs of control
1. Introduction There is a wide-spread belief in human resource management and the popular business press that exerting control can damage worker performance by eroding motivation and willingness to cooperate.1 This view is consistent with numerous empirical studies from psychology and organizational economics.2 In their prominent study Falk and Kosfeld (2006) investigate such hidden costs of control in an experimental work relationship. Workers can exert costly effort to increase the payoffs of their bosses. Before workers choose effort, bosses decide whether or not to control workers. Imposing control forces workers to exert at least some minimum effort. If workers maximize their own payoffs, they exert the least effort possible to save on effort costs. Falk and Kosfeld find that although many workers indeed always choose the least effort possible, a substantial fraction of workers exert less effort if controlled than if not controlled. Exerting control in fact reduces average effort contributions.3
∗ Correspondence address: Goethe University Frankfurt, Grueneburgplatz 1, 60323 Frankfurt am Main, Germany. Tel.: +49 69 79834815. E-mail address: [email protected] 1 See, for example, Manzoni and Barsoux (1998) and Herzberg (2003) who stress the negative consequences of exerting tight control over employees. Foss (2003) provides a careful case study on the detrimental effects of such micro-management. 2 The extensive empirical literature on monitoring and motivational crowding-out includes Plant and Ryan (1985), Barkema (1995), and Dickinson and Villeval (2008). Further, Enzle and Anderson (1993), Ariely et al. (2008), and Dominguez-Martinez et al. (2010) show that individuals dislike being controlled, and do not dislike being monitored as such. Together these studies document the existence of hidden costs of control. Ryan and Deci (2000) and Frey and Jegen (2001) discuss some theoretical foundations for hidden costs of control, and they provide numerous additional references. 3 Although there is some debate in the literature concerning the magnitude of the effect, an increasing number of studies provide experimental evidence for the existence of hidden costs of control. See in particular Schnedler and Vadovic (2011) and Charness et al. (2012). 0167-2681/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jebo.2013.04.017
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Since choosing high effort remains feasible even when being controlled, such hidden costs of control are incompatible with transitive preferences defined exclusivly over payoff outcomes. Theoretical economic explanations for the observed behavior are therefore almost all based on signaling models.4 However, these explanations can only be relevant if firms have some informational advantage over workers. This is not reasonable in all the circumstances in which there exist hidden costs of control. The present paper complements the existing literature by showing that intentionbased reciprocity can be an alternative explanation for hidden costs of control. This new explanation is not based on signaling. The present analysis further qualifies the wide-spread opinion that intention-based reciprocity is inconsistent with hidden costs of control. At first it might seem very natural to think that workers consider the mere act of not being controlled as kind, and then reciprocate not being controlled with high effort. Yet Falk and Kosfeld (2006, p. 1616) rightly argue that this is inconsistent with existing models of intention-based reciprocity. The reason is that exerting no control has to be considered unkind if uncontrolled workers exert higher effort and thus receive lower payoffs than controlled workers. In other words: if everybody expects workers to always reciprocate not being controlled with particularly high effort, then not exerting control is no longer kind because it reduces the payoff of workers, and thus cannot trigger high effort as reciprocal reaction. The present paper shows that – with a simple extension of the basic model – intention-based reciprocity can explain hidden costs of control. The only requirements are that individuals differ in their propensity for reciprocity, and that preferences are private information.5 After exploring the proposed extension in a more general setup, the model considers a simplified version of the control game from Falk and Kosfeld. The key assumption is that some workers are purely selfish in the sense that they only care for their own monetary payoffs, whereas other workers are reciprocal in the sense of Rabin (1993) and Dufwenberg and Kirchsteiger (2004). They are thus willing to incur some monetary costs to reciprocate kind actions with kind actions. Preferences are private information. The analysis shows that if reciprocal workers are sufficiently reciprocal and the fraction of selfish workers is sufficiently high, there exists a pure-strategy reciprocity equilibrium in which (i) selfish workers always choose the minimum feasible effort, whereas (ii) reciprocal workers choose lower effort if controlled than if not controlled. This equilibrium is based on the following intuition. On the one hand, exerting no control would be unkind if all workers were reciprocal, because then all workers would reciprocate no control with high effort. On the other hand, exerting no control would be kind if all workers were selfish, since then all workers would shirk and consequently get high payoffs. For the existence of the above reciprocity equilibrium, it is thus crucial that workers’ preferences are not only heterogeneous but also private information. In this case bosses do not know their workers’ preferences, and workers know that bosses do not know their workers’ preferences, thus workers must form beliefs concerning the kindness of their bosses’ actions. For this they put themselves into the shoes of their bosses, taking into account only the information that bosses actually have when taking their control decisions. Workers thus derive the average kindness of particular actions. If most workers are rightly expected to be selfish, reciprocal workers might consider it to be on average kind to be left uncontrolled. Reciprocal workers consequently reciprocate not being controlled with high effort. It is important to note that exerting no control is not considered to be kind by reciprocal workers because it provides other selfish colleagues with the opportunity to shirk. Workers have no colleagues in the considered situations. Instead, workers take into account that their bosses rationally believe them to be predominantly selfish! Exerting no control is therefore considered to be kind because (i) it provides also reciprocal workers with the opportunity to get a high payoff by shirking, (ii) this opportunity is not purely hypothetical, since everybody knows that most workers shirk if not controlled, and (iii) bosses do not know workers’ types, and thus risk getting low payoffs by forsaking control. In essence, not controlling workers is kind, exactly because this kindness might not be reciprocated. For illustration of the underlying theoretical mechanism, consider the following example. Suppose a new acquaintance visits your home for dinner. Social convention requires the guest to bring a bottle of wine. Unfortunately, your new acquaintance does not know your preferences concerning white or red wine, and you are aware of this ignorance. It is also commonly known that people typically prefer red wine. But you actually prefer white wine. Would you consider your guest bringing red wine as unkind? The present model would argue that bringing red wine is – given the incomplete information on your preferences and prior beliefs – actually kinder than bringing white wine. This holds even though you actually prefer white wine. The following example further illustrates the importance of incomplete information for the argument. Suppose an employer decides to provide all male workers with a pay rise, while keeping the pay for female workers unchanged. Could this be considered as on average kind by female workers, if the vast majority of employees is male? After all, every worker had a 50% chance of being male at birth. According to the present model, the answer is negative, because gender is observable. Every female worker thus knows that denying a pay rise to female employees is unkind to her, because the employer knows her gender, and therefore knows exactly the unkind consequences of his decision on her pay.
4
The related economics literature is discussed at length in Section 2. The empirical evidence clearly shows that individuals differ in their reciprocal or social preferences. See, for example, Fischbacher and Gächter (2010). Heterogeneity is also an important theoretical component in other model of social preferences. For example, Fehr et al. (2008) and Fehr and Schmidt (2000) show that inequity aversion à la Fehr and Schmidt (1999) is consistent with the laboratory evidence only via the strategic interaction between selfish and inequity averse individuals. 5
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The paper finally illustrates an implicit assumption that follows from the application of existing models of reciprocity, but becomes particularly critical in the presence of incomplete information. This assumption is that reciprocal workers do not dislike selfish workers, and do not use any evaluation of the behavior of selfish workers to assess the kindness of their bosses. Exerting no control is considered to be kind by reciprocal workers, because these workers would also receive a high payoff if they were selfish themselves. But suppose that reciprocal workers would like bosses to punish all selfish behavior, because reciprocal workers also dislike selfish workers. This might imply that reciprocal workers would like bosses to punish them if they were selfish themselves. In that case exerting no control might be considered to be morally wrong, and thus in some sense not deserving high effort as reciprocal response. The implicit assumption in the present specification therefore is that workers should believe that all workers – including themselves – have the right to behave however they want. Consequently, any evaluation of worker behavior does not affect the kindness assigned to the behavior of bosses. 2. Related literature The present analysis adds to the theoretical literature on crowding-out by providing a new rationale for hidden costs of control. In contrast to the present model, all prominent existing explanations are based on signaling. Most closely related are Sliwka (2007) and Ellingsen and Johannesson (2008) who explicitly refer to the control game from Falk and Kosfeld. In Sliwka (2007) bosses signal that there is a high fraction of steadfast fair-minded workers by exerting no control. This induces conformist workers – who want to comply with the prevalent social norm among steadfast workers – to exert high effort. Ellingsen and Johannesson (2008) argue that bosses signal their altruism by exerting no control. This makes it more desirable for workers to signal their altruism. For this signaling to be credible, altruistic workers have to work harder if not controlled than if controlled. These studies complement an extensive signaling literature on motivational crowding-out. The following incomplete list of articles summarizes some of the most popular arguments. In Spier (1992) bosses might leave contracts incomplete – wages do not condition on project outcomes – to signal that the job environment is more likely to yield favorable outcomes. This facilitates worker participation. Bénabou and Tirole (2003) focus on effort choices. Bosses signal that workers’ effort is less productive by opting for strong monetary incentives or control. Although monetary incentives increase motivation in the short run, in the long run the effect is detrimental. In Suvorov and van de Ven (2009) bosses transmit performance information by paying discretionary bonuses. This conveys information on workers’ ability, which in turn affects workers’ future effort decisions. Herold (2010) argues that bosses signal their trust in workers by leaving contracts incomplete. Bosses’ beliefs affect their own effort contributions, which in turn influence workers’ effort choices. In Friebel and Schnedler (2011) bosses signal the intrinsic motivation of some team members by empowering workers. This increases effort by other team members due to complementarities in production. In contrast to all these papers, the present explanation for hidden costs of control is not driven by bosses signaling anything, because in the present context bosses have no private information. The present model can also be distinguished empirically from the signaling explanations of hidden costs of control. Signaling only works if bosses have information that is relevant for workers. This assumption is not always equally plausible. In stable environments experienced workers could have gathered a lot of information on prevalent social norms and the fraction of fair-minded steadfast workers. Experienced workers might also know themselves and their job environment. The altruism of bosses could have been revealed by previous behavior towards other workers and stakeholders. Getting additional information in these situations – via the control choices of bosses – might then have no big impact on beliefs. There should be only limited hidden costs of control. Arguably, also experienced workers react adversely to being controlled. For this case, only the present explanation based on intention-based reciprocity predicts an undiminished deterioration of cooperation.6 The present analysis further complements economic theory on intention-based reciprocity by studying private information on heterogeneous reciprocity concerns. Rabin (1993, p. 1296) argues that “Extending the model to incompleteinformation games is essential for applied research, but doing so will lead to important new issues.” Further, he conjectures that incomplete information might strongly affect results and thus predictions. Geaneakoplos et al. (1989, pp. 67–68) and Battigalli and Dufwenberg (2009) indicate how psychological game theory might encompass private information. The present paper adds to this literature by introducing private information on individual reciprocity concerns. The particular specification is fruitfully applied to a popular research question in organizational economics, and thereby illustrates some of the arising conceptual issues. It corroborates the view that including incomplete information might affect results, since hidden costs of control arise in equilibrium only if reciprocity preferences are private information. Moreover, the study reconciles intention-based reciprocity with the empirical evidence on mutually beneficial conditional cooperation in social dilemmas.7 Such mutually beneficial conditional cooperation is incompatible with the standard intention-based reciprocity model by Rabin (1993), because according to his definition, an action cannot be kind, if it increases
6 However, the present explanation requires that the reciprocity preferences of experienced workers are private information. In the considered situations it must thus be possible to learn the altruism of bosses – because their contract choices are easily observable – whereas it is difficult to learn the reciprocity preferences of workers – because their effort choices are not easily observable. 7 See, for example, Clark and Sefton (2001) on conditional cooperation in a sequential prisoners’ dilemma. They find that extent of conditional cooperation makes it indeed optimal for the first mover to cooperate.
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the equilibrium payoff of everybody, including those taking that action. The reason is that in this case kind and selfish intentions cannot be separated. Rabin’s (1993, pp. 1296–1297) argument is generalized by Netzer and Schmutzler (2012). They show for a large class of games that there cannot be mutually kind behavior in any fairness equilibrium if at least one individual is selfish. This holds because selfish individuals by definition maximize their own payoffs. Their equilibrium actions can therefore be considered at best kindness neutral. The present paper shows that Rabin’s fairness specification can be consistent with profitable conditional cooperation in, for example, the sequential prisoners’ dilemma, if it accounts for private information on heterogeneous reciprocity preferences. The argument runs as follows. There are reciprocal individuals who respond to cooperation with cooperation. Cooperation is kindness neutral towards these individuals if ultimately everyone is better off. But there are also selfish individuals who do not reciprocate cooperative behavior. Cooperation is kind towards these individuals, because it increases their payoffs at the expense of the cooperating individuals. If cooperation is risky – because many individuals are selfish and do not reciprocate – then cooperation might be on average kind, even if it is on average profitable to cooperate. 3. Model This section develops theoretical foundations. Apart from the control game analyzed later, the setup covers many applications that are of interest in organizational economics, including gift exchange and other simple deterministic moral hazard situations. Ignoring incomplete information, the basic strategic situation can be characterized as follows. One boss interacts with one worker. First, the boss chooses some action ab ∈ Ab from a finite set of actions Ab . These actions can be control choices or contract offers. The worker observes the decision of the boss and then decides on his action aw ∈ Aw (ab ) from some finite sets of actions Aw (ab ). These actions could be contract acceptance and effort choices. The sets of feasible actions for the worker might depend on the prior choice of the boss. Monetary payoffs are determined by actions, where b (ab , aw ) is the payoff of the boss and w (ab , aw ) is the payoff of the worker given the actions (ab , aw ). The crucial assumptions in this paper are that (i) workers can differ in their propensity for reciprocity concerns, while (ii) their individual preferences are private information. Workers can be either selfish or reciprocal, so that the type space is = {s, r}. Individual types ∈ are private information, but it is common knowledge that workers are of type with prior probability () ∈]0, 1[. With two types this implies (r) = 1 − (s). Selfish workers are only interested in their own payoff. Reciprocal workers have intention-based fairness concerns in the spirit of Rabin (1993) and Dufwenberg and Kirchsteiger (2004). Market competition arguably forces firms – and thus bosses – to maximize profit. It is thus assumed for simplicity that all bosses are selfish. A working paper version of the present analysis shows that allowing for reciprocal bosses has no substantial impact on the results in the control game studied later.8 Reciprocal workers’ utility is not fully determined by the above payoffs, but also depends on strategies and beliefs concerning strategies. Like the existing literature on intention-based reciprocity, the present paper focuses on pure strategies.9 A fully specified pure strategy for the boss is simply a decision ˛b ∈ Ab . A fully specified strategy for the worker is a function ˛w : × Ab → Aw (ab ) that specifies feasible type-dependent decisions conditional on the observed choices of bosses. Beliefs will also be crucial for the analysis. Define ˇw as the belief of bosses concerning the strategy of workers, and let w be the belief of workers concerning the belief of bosses concerning the strategy of workers. Further, denotes the probabilities with which bosses believe to be facing workers with certain types, and describes the belief of workers concerning the probabilities with which bosses believe to be facing workers with certain types. 3.1. Kindness with incomplete information on workers’ reciprocity The present paper applies the definitions of reciprocity by Rabin (1993) and Dufwenberg and Kirchsteiger (2004) while accounting for incomplete information on workers’ reciprocity preferences.10 As with complete information, the kindness of an action is assessed by putting the payoff consequences of that action in relation to the set of payoff consequences that could have been achieved via alternative actions. Incomplete information comes into the picture since the same action can have different payoff consequences for selfish and reciprocal workers.
8 See von Siemens (2011). The only difference to the present study is that reciprocal bosses’ control choices are influenced by their fairness concerns. This can explain heterogeneous control choices even though in equilibrium all bosses and workers share the same consistent beliefs concerning workers’ equilibrium behavior. 9 It is not trivial to evaluate the kindness of an observed action resulting from a mixed strategy, as it could depend on whether mixed strategies are viewed as deliberate mixing by an individual or as a description of the behavior of a population with heterogeneous individuals using different pure strategies. For some theory and experimental evidence on this complicated matter see Aldashev et al. (2010). Further, the intentions of any observed actions will be interpreted as if behavior was always fully deliberate. This seems more appropriate in the context of pure strategies. For further discussion, see Rabin (1993, p. 1286), Dufwenberg and Kirchsteiger (2004, p. 275 and pp. 279–280), and Segal and Sobel (2007, pp. 209–210). 10 Results are largely indifferent to the exact specification of reciprocity preferences. In particular, it does not really matter whether the definition of kindness follows Rabin (1993) and Dufwenberg and Kirchsteiger (2004). A discussion of the implications of different reciprocity concepts is thus deferred to Section 5.
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Consider first the kindness of workers’ actions towards bosses who have chosen some arbitrary action ab ∈ Ab . Let ˘ b (ab ) ˜ b (ab ) be be the set of payoff combinations that workers can then implement by choosing some actions aw ∈ Aw (ab ). Let ˘ the Pareto-efficient frontier of this set of payoff combinations. Let bh (ab ) and b (ab ) be the highest and lowest payoffs
for bosses from this set of Pareto-efficient payoff combinations. Define be (ab ) = (bh (ab ) + b (ab ))/2 as the equitable payoff. This equitable payoff characterizes the kindness-neutral payoff benchmark.11 Let bmin (ab ) be the minimum payoff for bosses from the set ˘ b (ab ). Note that this minimum payoff might originate from a Pareto-dominated payoff combination. Then kwb (ab , aw ) =
b (ab , aw ) − be (ab ) bh (ab ) − bmin (ab )
(1)
is the kindness of workers with action aw towards bosses with action ab . This definition applies whenever the denominator is not equal to zero. Otherwise, workers cannot influence bosses’ payoffs, and all actions are assigned a kindness of zero. The kindness of workers’ actions depends on the set of feasible payoff combinations and thus on bosses’ actions. Moreover, beliefs about strategies are irrelevant since workers know exactly the payoff consequences of their actions. Consider next the kindness of certain actions chosen by bosses. To simplify the exposition, first assume that it is common knowledge that workers follow strategy ˛w while fraction () of workers has preferences ∈ . As in Dufwenberg and Kirchsteiger (2004) any choices by bosses are considered to be fully intentional. The kindness of bosses’ actions then depends on the resulting payoffs for workers. Reciprocal and selfish workers might respond differently to the same control choices. Further, bosses cannot know their workers’ types, and this is common knowledge among bosses and workers. This poses the question of how to include incomplete information on workers’ preferences in a model with intentionbased reciprocity. The main idea is that the kindness of an action is determined by the information available to the individuals taking that action. Workers thus first derive the kindness of an action separately towards workers with selfish and reciprocal preferences, that is, towards workers with particular action responses. They then compute the sum of the type-dependent kindnesses towards selfish and reciprocal workers, weighted with the respective probabilities with which bosses believe to be facing these types of workers. Workers simply form the expected kindness of an action.12 This idea is reflected in the formal definitions as follows. Given that workers employ strategy ˛w define ˘w (˛w , ) as the set of payoff combinations that bosses can implement when paired with workers of type ∈ by choosing actions ˜ w (˛w , ). The resulting payoffs h (˛w , ), (˛w , ), ab ∈ Ab . This set of payoff combinations has Pareto-efficient frontier ˘ w w e (˛ , ), and min (˛ , ) are defined analogously to the above definitions. Then w w w w kbw (ab , ˛w , ) =
e (˛ , ) w (ab , ˛w (, ab )) − w w h (˛ , ) − min (˛ , ) w w w w
(2)
is the kindness of action ab towards workers with type if workers employ strategy ˛w . The kindness of an action ab is normalized to zero whenever the denominator is zero. Given workers’ strategy ˛w it is possible to compute the kindness of an action ab towards all types of workers ∈ . Then
() kbw (ab , ˛w , )
(3)
∈
is the expected kindness of bosses choosing action ab . Following Rabin (1993) and Dufwenberg and Kirchsteiger (2004), the kindness of an action thus follows from equilibrium payoff consequences. The definition does not take into account that reciprocating an unkind action might create utility in itself, for example, by arousing strong spiteful emotions. Otherwise, being unkind might turn out to be kind, if the resulting spiteful emotions are sufficiently strong. Moreover, the kindness of an action does not depend on the payoffs that workers could have obtained by deviating from their equilibrium strategy. This is driven by the idea that in equilibrium individuals should hold expectations that are consistent with equilibrium behavior. Segal and Sobel (2007) propose another definition of reciprocity that accounts for payoffs that can only be obtained off equilibrium. The difference between the present and their approach is further discussed in Section 5. The above definitions are based on the assumption that it is common knowledge that workers employ strategy ˛w and are of type ∈ with probability (). If bosses assess the kindness of their own actions, then in general their assessment depends on their belief ˇw concerning the strategy of workers, and on the probabilities with which they believe workers to be of certain types. If workers assess the kindness of actions taken by bosses, then in general their assessment depends on
11 Due to the restriction to Pareto-efficient payoff combinations, an action that increases payoffs for everybody must be assessed as kindness-neutral. Exactly this definition makes it impossible in the basic model by Rabin to explain mutually beneficial cooperation as equilibrium phenomenon in social dilemmas. 12 An alternative approach would be to treat type-dependent pure strategies as if worker were using mixed strategies. In the control game studied later, exerting no control can then be assessed as kind if it provides workers with higher and bosses with lower expected payoffs than exerting control. Mutually profitable conditional cooperation is no longer possible, see the discussion in the introduction. Otherwise, results are largely robust to this alternative specification. However, viewing individuals as using mixed strategies only seems plausible if in equilibrium individuals are almost indifferent between the relevant actions. In the control game studied later this need not be the case with selfish and reciprocal individuals, since the reciprocal action might result in substantially lower monetary payoffs than the selfish action.
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their belief w concerning the belief of bosses concerning the strategy of workers, and on the beliefs with which workers believe bosses to believe workers to be of certain types. The more general definition of kindness then follows from the above, where ˛w and in (2) and (3) are replaced with the corresponding first-order and second-order beliefs. 3.2. Preferences Given action ab and the involved beliefs and ˇw define Ub (ab , ˇw , ) =
() b (ab , ˇw (, ab ))
(4)
∈
as the expected utility of bosses. Bosses simply care for their expected monetary payoff. The utility of workers given their action aw , action ab by their bosses, and beliefs w and concerning the beliefs of bosses, is defined as Uw (aw , ab , w , ) = w (ab , aw ) + () kwb (ab , aw )
() kbw (ab , w , )
(5)
∈
where () ∈ IR+ characterizes the relative importance of reciprocity concerns for workers with type ∈ . It is assumed that
(r) > (s) = 0. Reciprocal workers thus care for their own expected payoffs, but they also care for fairness. Selfish workers only care for their own expected payoffs. Bosses and workers maximize expected utility. 3.3. Reciprocity equilibrium The equilibrium notions of Rabin (1993) and Dufwenberg and Kirchsteiger (2004) are adapted to the present context with incomplete information as follows. ∗ , ˛∗ , ∗ , ∗ , ∗ ) is characterized by Definition 1 (Reciprocity equilibrium). A reciprocity equilibrium (˛∗b , ˇw w w
˛∗b
∈ argmax a∈Ab
∗
∗ () b (a, ˇw (, a))
,
˛∗w (, ab )
(6)
∈
∈ arg max
a∈Aw (ab )
w (ab , a) + () kwb (ab , a)
∗
∗ () kbw (ab , w , )
(7)
∈
∗ = ∗ , * = * = . for all ∈ and ab ∈ Ab , and ˛∗w = ˇw w
First, equilibrium strategies maximize expected utility given all equilibrium strategies, given bosses’ equilibrium firstorder beliefs, and given workers’ equilibrium second-order beliefs. Second, first-order and second-order beliefs are consistent with prior beliefs and equilibrium strategies. Thirdly, the above holds at all decision nodes – that is after seeing any initial choice by bosses. This implies that equilibria cannot be based on unreasonable behavior off the equilibrium path. Fourthly, the definitions imply that the kindness of actions is assessed under the assumption that any observed actions are fully intentional. 4. Control game The remainder of the paper applies the developed general concept to study hidden costs of control. The strategic situation is as follows. First, the boss decides whether or not to control the worker, ab ∈ Ab = {c, nc}. Control is costless. The worker observes the decision of the boss and then decides on his effort aw . Effort can be high, medium, or low. The set of possible effort choices Aw (ab ) depends on the control decision ab of the boss, where Aw (c) = {h, m} and Aw (nc) = {h, m, }. By controlling the worker, the boss can thus prevent the worker from exerting low effort. The worker’s effort choice determines both his payoff and the payoff of the boss via the payoff functions b : Aw → IR and w : Aw → IR. More effort strictly increases the payoff of the boss and strictly decreases the payoff of the worker, thus b (h) > b (m) > b ( ) and w ( ) > w (m) > w (h). The sequence of actions is summarized in Fig. 1. All bosses are selfish, whereas workers are either selfish or reciprocal. A fully specified pure strategy for bosses is a control choice ˛b ∈ Ab . A fully specified strategy for workers is a function ˛w : × Ab → Aw (ab ) that specifies type-dependent effort choices conditional on bosses’ control choices. To avoid tedious and uninformative case distinctions, the following cutoff rule is implemented in the equilibrium analysis of the control game: in case of indifference workers choose the lower effort, and bosses control their workers. This makes it harder to achieve the goal of the study – to find an equilibrium in which some bosses do not control while reciprocal workers reciprocate not being controlled with exerting high effort.
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Fig. 1. Control game.
4.1. Hidden costs of control This section derives the existence conditions for a reciprocity equilibrium in which reciprocal workers reciprocate not being controlled by exerting high effort. Since the kindness of workers towards bosses does not depend on any beliefs or types, (1) implies the following in any equilibrium. Lemma 1 (Kindness of worker). In any reciprocity equilibrium 1 kwb (c, m) = − ; 2
kwb (c, h) = +
1 2
1 kwb (nc, ) = − ; 2
kwb (nc, m) =
(8)
and 2 b (m) − b (h) − b ( ) ; 2(b (h) − b ( ))
kwb (nc, h) = +
1 2
(9)
characterize the kindness of workers towards bosses. A selfish worker always maximizes his payoff, and therefore chooses the minimum possible effort. This directly implies the following. Lemma 2 (Behavior selfish workers). In any reciprocity equilibrium ˛∗w (s, nc) = and
˛∗w (s, c) = m
(10)
characterize the equilibrium behavior of selfish workers. max (˛∗ , s) = ( ), Since the behavior of selfish workers is identical in all equilibria, Lemma 2 yields directly w w w min (˛∗ , s) = (m), and e (˛∗ , s) = ( ( ) + (m))/2. This implies that controlling a selfish worker is unkind, whereas w w w w w w w not controlling a selfish worker is kind.
Lemma 3 (Kindness of bosses towards selfish workers). In any reciprocity equilibrium kbw (nc, ˛∗w , s) = +
1 2
and
kbw (c, ˛∗w , s) = −
1 2
(11)
characterize the kindness of bosses towards selfish workers. Before presenting the main result define
˜1 =
w ( ) − w (h) 1 − 2
(12)
˜2 =
2(w (m) − w (h))(b (h) − b ( )) . (1 − 2)(b (h) − b (m))
(13)
and
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Further, define ˜ = b (m) − b ( ) . b (h) − b ( )
(14)
The main result is made formally precise in the following proposition. Proposition 1 (High effort reciprocation). Consider a reciprocity equilibrium in which reciprocal workers reciprocate not being controlled so that ˛∗w (r, nc) = h and ˛∗w (r, c) = m. Selfish workers behave as characterized in Lemma 2. Then the following holds. 1 Such an equilibrium exists if and only if (r) < 1/2 and (r) > max{
˜ 1,
˜ 2 }. ˜ 2 Bosses choose control if and only if (r) ≤ . max (˛∗ , r) = (m) and min (˛∗ , r) = (h) so that e (˛∗ , r) = ( (m) + Proof. Workers’ equilibrium behavior yields w w w w w w w w w w (h))/2. Concerning the kindness of bosses towards reciprocal workers this yields kbw (nc, ˛∗w , r) = −1/2 and kbw (c, ˛∗w , r) = 1/2. The expected kindness of bosses towards workers with unknown type is then
()kbw (c, ˛∗w , ) = (r) − 1/2 and
∈
()kbw (nc, ˛∗w , ) = 1/2 − (r).
(15)
∈
Consider the optimality of the equilibrium behavior of bosses and workers. Consider first workers. The behavior of selfish workers is optimal given Lemma 2. Given the cutoff rule the behavior of reciprocal workers is optimal if and only if w (h) + (r)
w (h) + (r)
1 2
1 2
1
− (r)
1
− (r)
w (m) − (r) (r) −
2
1 2
2
> w ( ) − (r)
2
> w (m) + (r)
1 2
1
1
2
1
− (r)
(16)
2
2 (m) − (h) − ( ) b b b
− (r)
≥ w (h) + (r) (r) −
1 2
2(b (h) − b ( ))
1 2
.
(17)
(18)
Constraints (16) and (17) ensure that if not controlled, reciprocal worker prefer to exert high rather than medium or low effort. (18) ensures that if controlled, reciprocal workers prefer to exert medium rather than high effort. As w (h) < w ( ) constraint (16) can hold only if (r) < 1/2. This condition with w (m) > w (h) implies that (18) can be ignored. Rearranging (16) yields as condition (r) >
˜ 1 and rearranging (17) yields (r) >
˜ 2 . Note that since b (h) − b ( ) > b (h) − b (m) it is not clear whether (16) or (17) is binding even though w ( ) − w (h) > w (m) − w (h). Consider next the optimality of the equilibrium behavior of bosses. The condition on (r) simply follows from comparing expected payoffs when controlling and not controlling. The intuition for this result is as follows. If workers are selfish with high probability – the ex ante probability (r) to be reciprocal is smaller than 1/2 – then controlling workers with unknown type is on average unkind, whereas not controlling workers with unknown type is on average kind. If reciprocal workers sufficiently care for reciprocity – the reciprocity parameter (r) exceeds a certain threshold – then they reciprocate not being controlled by exerting high effort. Note that the exact cutoff values for (r) and (r) clearly depend on the specification of reciprocity preferences. With an alternative specification like Falk and Fischbacher (2006) there might exist similar equilibria even if the majority of workers are reciprocal. The same holds true if the kindness of an action is not normalized as in Rabin (1993) but depends on absolute payoff differences as in Dufwenberg and Kirchsteiger (2004). Further, in equilibrium it can be optimal for bosses to exert control although reciprocal workers would exert high effort if they were not controlled. Such an equilibrium exists if and ˜ 1/2}. Exerting no control then does not pay, either because too few workers are reciprocal, or because only if (r) ≤ min{, exerting high rather than medium effort does not increase payoffs sufficiently. The reciprocity equilibrium as characterized in Proposition 1 exhibits the most important qualitative features of hidden costs of control as observed in the empirical studies. In contrast to all prominent theoretical explanations for hidden costs of control, signaling cannot play any role, because bosses possess no private information. 4.2. All other pure-strategy reciprocity equilibria This section shows that in the present context there exist only rather intuitive reciprocity equilibria in pure strategies. The focus is on the intuition; all technical details are available upon request. Proposition 1 describes the reciprocity equilibrium for high levels of reciprocity. For medium levels of reciprocity there exists a reciprocity equilibrium in which reciprocal workers always exert medium effort. Not exerting control is then kind to selfish workers, and kindness neutral to reciprocal workers. Reciprocity concerns have to be sufficiently strong such that reciprocal workers do not exert low effort if they are not controlled, but they must also be sufficiently weak such that reciprocal workers do not exert high effort if they are not controlled. Bosses always control since not controlling never
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increases effort, not even for reciprocal workers. For low levels of reciprocity, there exists a reciprocity equilibrium in which reciprocal and selfish workers behave in the same way: they always choose the least effort possible. Not controlling is kind to all types of workers. However, reciprocity concerns are weak so that even unambiguously kind actions cannot trigger effort choices that exceed low effort. Bosses control because this increases effort contributions from both selfish and reciprocal workers. There exist no other reciprocity equilibria in pure strategies. The reason is that in any other equilibrium reciprocal workers would have to exert high effort once controlled. This can only be optimal if controlling workers is considered to be kind. The latter is never the case for selfish workers. It also cannot be kind to reciprocal workers for the following reason. Reciprocal workers cannot exert more than high effort if they are not controlled. Thus, exerting control is at most kindness neutral towards reciprocal workers. But then reciprocal workers maximize their payoffs and do not exert more than the minimum effort. This demonstrates that the theory possesses predictive power: reciprocal workers never exert more than the least effort possible if they are controlled. 5. Further related literature This section discusses some aspects of the current model specification by connecting results to further related literature. Particularly, it shows that the main result – in equilibrium some workers might respond to control by lowering their effort – is quite robust with respect to the exact specification of reciprocity preferences. In contrast to the present specification, Falk and Fischbacher (2006) assume that reciprocity preferences are influenced by payoff inequality. Workers consider a control choice as kind if and only if they consequently receive higher payoffs than their bosses. The following argument demonstrates that using this definition of reciprocity does not change results fundamentally. Suppose reciprocal workers reciprocate not being controlled with high effort. Reciprocal workers consider not being controlled as kind if the resulting payoff difference w (h) − b (h) is positive. But since in equilibrium they then exert only medium effort, being controlled is even kinder to reciprocal workers. The reason is that the payoff difference w (m) − b (m) exceeds w (h) − b (h). Further, since w (h) is the minimum payoff bosses can grant workers in equilibrium, the kindness of choosing no control is further reduced to capture intentions. As the present specification, Falk and Fischbacher (2006) thus imply that exerting no control is less kind towards reciprocal workers than exerting control. However, selfish workers choose low effort if not controlled and medium effort if controlled. Towards selfish workers exerting no control is kinder than exerting control. If the kindness of bosses is the weighted sum of the kindness of bosses towards selfish and reciprocal workers, then exerting no control can be considered as kind, if and only if the fraction of reciprocal workers (r) is below some cutoff. The present equilibrium arguments then apply. The only major difference is that the cutoff for (r) depends on payoffs and can differ from 1/2. There might thus exist an equilibrium in which a majority of workers exert high effort when not being controlled. Segal and Sobel (2007, pp. 206–209) take a rather different approach towards reciprocity. They argue that the kindness of a control choice depends on the resulting maximum feasible payoff for workers. This definition implies that no control is kinder than control, because only no control allows workers to get the highest payoff by shirking. But with homogeneous workers this definition of kindness – kindness depends on what workers could do, but not an what they actually do – implies that a control choice can be kind even if the subsequent equilibrium result is unfavorable for workers. With heterogeneous reciprocity concerns, there exist selfish workers that in equilibrium do abuse every opportunity to maximize their own payoffs. Allowing for private information on heterogeneous reciprocity concerns thus in some sense reconciles the definitions of kindness from Rabin (1993) and Segal and Sobel (2007). The only remaining difference to Segal and Sobel (2007) is that the fraction of selfish workers influences the kindness of bosses’ control choices. Schnedler and Vadovic (2011) sketch how hidden costs of control might be caused by guilt aversion in the spirit of Battigalli and Dufwenberg (2007). Bosses could expect – because of social norms or the framing of the decision environment – that workers exert less effort if controlled than if not controlled. Guilt averse workers match these expectations, so that behavior and expectations are consistent in equilibrium. However, in such models of guilt aversion it seems to be a priori unclear what might constitute reasonable expectations. In particular, there might also exist an equilibrium in which bosses rightly expect workers to exert higher effort if controlled than if not controlled. Rabin (1993, p. 1285) argues that one advantage of intention-based reciprocity is that it derives all behavioral components – the psychological game – from the material payoffs of the underlying strategic interaction. Section 4.2 shows that this approach rules out unreasonable equilibria. The present analysis thus demonstrates that despite restrictions on reasonable equilibrium behavior, intention-based reciprocity might well explain hidden costs of control if there is incomplete information on individual reciprocity preferences. 6. Conclusion The present paper shows that intention-based reciprocity can explain hidden costs of control if individuals differ in their propensity for reciprocity concerns while preferences are private information. This complements the existing theoretical literature by offering an explanation for hidden costs of control that is not based on signaling. The present study also extends existing models of intention-based reciprocity by introducing private information on heterogeneous reciprocity concerns. It demonstrates that this extension generates new predictions that are consistent with the empirical evidence on profitable conditional cooperation. Unobservable heterogeneity seems to be very plausible in most economic situations – including
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all laboratory experiments. This creates ample scope to further explore the extended explanatory power of intention-based reciprocity in future applications. Finally, the analysis complements a recent strand of papers that apply models of reciprocity, conditional altruism, and conditional cooperation. von Siemens (2009) shows how reciprocity can improve investment incentives in a hold-up situation. I˙ ris¸ and Santos-Pinto (2013) derive conditions under which reciprocity among managers facilitates or complicates collusion in the product market. Dur et al. (2010) and Dur and Sol (2010) investigate optimal incentive contracts if workers reciprocate the attention of managers or colleagues by exerting more effort. Netzer and Schmutzler (2012), Non (2012), and Englmaier and Leider (2013) study optimal monetary incentives if workers reciprocate overly generous employment contracts with higher effort. Non (2012) accounts for heterogeneous reciprocity concerns among workers, but builds his analysis on type-based reciprocity by Levine (1998) and not on intention-based reciprocity by Rabin (1993). Kosfeld and von Siemens (2009, 2011) show how firms can use incentive contracts to promote conditional cooperation among workers through worker selection. Finally, Sebald (2010) and Aldashev et al. (2010) argue that reciprocity concerns can influence not only optimal wage contracts but also appointment procedures. But none of these papers studies hidden costs of control as in Falk and Kosfeld (2006), and none of them investigates the impact of private information on heterogeneous reciprocity concerns in a model with intention-based reciprocity. Proponents of outcome-based social preferences often argue that theories of intention-based reciprocity suffer from serious drawbacks that include multiple – often counterintuitive – equilibria and a high degree of complexity. The present paper shows that these arguments are justified: applying reciprocity even in simple strategic situations raises substantial conceptual complications. But the present also demonstrates that these problems can be overcome. The application of intention-based reciprocity to economic problems – especially when outcome-based fairness concerns cannot explain the empirical evidence – might thus offer a fruitful avenue for future investigation. Acknowledgements Very helpful comments and suggestions from Josse Delfgaauw, Georg Kirchsteiger, Jurjen Kamphorst, Michael Kosfeld, Matthew Rabin, Wendelin Schnedler, Alexander Sebald, Randolph Sloof, Joep Sonnemans, Jeroen van de Ven, and two anonymous referees are gratefully acknowledged. References Aldashev, G., Kirchsteiger, G., Sebald, A., 2010. How (not) to decide: procedural games. ECORE Discussion Paper 2010/81. Ariely, D., Kamenica, E., Prelec, D., 2008. Man’s search for meaning: the case of legos. Journal of Economic Behavior and Organization 67, 671–677. Barkema, H.G., 1995. Do top managers work harder when they are monitored? Kyklos 48, 19–42. Battigalli, P., Dufwenberg, M., 2007. Guilt in games. American Economic Review (Papers and Proceedings) 97, 170–176. Battigalli, P., Dufwenberg, M., 2009. Dynamic psychological games. Journal of Economic Theory 144, 1–35. Bénabou, R., Tirole, J., 2003. Intrinsic and extrinsic motivation. Review of Economic Studies 70, 489–520. Charness, G., Cobo Reyes, R., Jiménez, N., Lacomba, J.A., Lagos, F., 2012. The hidden advantages of delegation: Pareto-improvements in a gift-exchange game. American Economic Review 102, 2358–2379. Clark, K., Sefton, M., 2001. The sequential prisoner’s dilemma: evidence on reciprocation. Economic Journal 111, 51–68. Dickinson, D., Villeval, M.C., 2008. Does monitoring decrease work effort? the complementarity between agency and crowding-out theories. Games and Economic Behavior 63, 56–76. Dominguez-Martinez, S., Sloof, R., von Siemens, F.A., 2010. Monitoring your friends, not your foes: strategic ignorance and the delegation of real authority. CESifo Working Paper Series No. 3172. Dufwenberg, M., Kirchsteiger, G., 2004. A theory of sequential reciprocity. Games and Economic Behavior 47, 268–298. Dur, R., Non, A., Roelfsma, H., 2010. Reciprocity and incentive pay in the workplace. Journal of Economic Psychology 31, 676–686. Dur, R., Sol, J., 2010. Social interaction, co-worker altruism, and incentives. Games and Economic Behavior 69, 293–301. Ellingsen, T., Johannesson, M., 2008. Pride and prejudice: the human side of incentive theory. American Economic Review 98, 990–1008. Englmaier, F., Leider, S., 2013. Contractual and organizational structure with reciprocal agents. American Economic Journal: Microeconomics (forthcoming). Enzle, M.E., Anderson, S.C., 1993. Surveillant intentions and intrinsic motivation. Journal of Personality and Social Psychology 64, 257–266. Falk, A., Fischbacher, U., 2006. A theory of reciprocity. Games and Economic Behavior 54, 293–315. Falk, A., Kosfeld, M., 2006. The hidden costs of control. American Economic Review 96, 1611–1630. Fehr, E., Kremhelmer, S., Schmidt, K.M., 2008. Fairness and the optimal allocation of ownership rights. Economic Journal 118, 1262–1284. Fehr, E., Schmidt, K.M., 1999. A theory of fairness, competition, and cooperation. Quarterly Journal of Economics 114, 817–868. Fehr, E., Schmidt, K.M., 2000. Fairness, incentives and contractual choices. European Economic Review 44, 1057–1068. Fischbacher, U., Gächter, S., 2010. Social preferences, beliefs, and the dynamics of free riding in public goods experiments. American Economic Review 100, 541–556. Foss, N.J., 2003. Selective intervention and internal hybrids: interpreting and learning from the rise and decline of the oticon spaghetti organization. Organization Science 14, 331–349. Frey, B.S., Jegen, R., 2001. Motivation crowding theory. Journal of Economic Surveys 15, 589–611. Friebel, G., Schnedler, W., 2011. Team governance: empowerment or hierarchical control. Journal of Economic Behavior and Organization 78, 1–13. Geaneakoplos, J., Pearce, D., Stacchetti, E., 1989. Psychological games and sequential rationality. Games and Economic Behavior 1, 60–79. Herold, F., 2010. Contractual incompleteness as a signal of trust. Games and Economic Behavior 68, 180–191. Herzberg, F., 2003. One more time: how do you motivate employees? Harvard Business Review 81, 87–96. I˙ ris¸, D., Santos-Pinto, L., 2013. Tacit collusion under fairness and reciprocity. Games 4, 50–65. Kosfeld, M., von Siemens, F.A., 2009. Worker self-selection and the profits from cooperation. Journal of the European Economic Association (Papers and Proceedings) 7, 573–582. Kosfeld, M., von Siemens, F.A., 2011. Competition, cooperation, and corporate culture. RAND Journal of Economics 42, 23–43. Levine, D.K., 1998. Modeling altruism and spitefulness in experiments. Review of Economic Dynamics 1, 593–622. Manzoni, J.F., Barsoux, J.L., 1998. The set-up-to-fail syndrom: how bosses create their own poor performers. Harvard Business Review 76, 101–113. Netzer, N., Schmutzler, A., 2012. Explaining gift-exchange—the limits of good intentions. mimeo. University of Zurich.
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Non, A., 2012. Gift-exchange, incentives, and heterogeneous workers. Games and Economic Behavior 75, 319–336. Plant, R.W., Ryan, R.M., 1985. Intrinsic motivation and the effects of self-consciousness, self-awareness, and ego-involvement: an investigation of internally controlling states. Journal of Personality 53, 435–449. Rabin, M., 1993. Incorporating fairness into game theory and economics. American Economic Review 83, 1281–1302. Ryan, R.M., Deci, E.L., 2000. Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist 55, 68–78. Schnedler, W., Vadovic, R., 2011. Legitimacy of control. Journal of Economics and Management Strategy 20, 985–1009. Sebald, A., 2010. Attribution and reciprocity. Games and Economic Behavior 68, 339–352. Segal, U., Sobel, J., 2007. Tif for tat: foundations of preferences for reciprocity in strategic settings. Journal of Economic Theory 136, 197–216. Sliwka, D., 2007. Trust as a signal of a social norm and the hidden costs of incentive schemes. American Economic Review 97, 999–1012. Spier, K.E., 1992. Incomplete contracts and signalling. RAND Journal of Economics 23, 432–443. Suvorov, A., van de Ven, J., 2009. Discretionary rewards as feedback mechanism. Games and Economic Behavior 67, 665–681. von Siemens, F.A., 2009. Bargaining under incomplete information, fairness, and the hold-up problem. Journal of Economic Behavior and Organization 71, 486–494. von Siemens, F.A., 2011. Intention-based reciprocity and the hidden costs of control. Tinbergen Institute Discussion Paper 11-115/1.
Contents lists available at SciVerse ScienceDirect
Journal of Economic Behavior & Organization journal homepage: www.elsevier.com/locate/jebo
Intention-based reciprocity and the hidden costs of control Ferdinand A. von Siemens a,b,∗ a b
Goethe University Frankfurt, Grueneburgplatz 1, 60323 Frankfurt am Main, Germany CESifo, Poschingerstrasse 5, 81679 Munich, Germany
a r t i c l e
i n f o
Article history: Received 20 November 2012 Received in revised form 23 April 2013 Accepted 23 April 2013 Available online 10 May 2013 JEL classification: A13 C70 D63 D82 L20
a b s t r a c t Empirical research suggests that – despite strengthening conventional incentives to put in effort – exerting control might reduce worker performance. The present paper shows that intention-based reciprocity can explain such hidden costs of control if individuals differ in their propensity for reciprocity and preferences are private information. Not being controlled might then be considered to be kind, because not everybody reciprocates not being controlled with high effort. This argument contrasts existing theoretical wisdom on the hidden costs of control that is almost exclusively based on signaling. © 2013 Elsevier B.V. All rights reserved.
Keywords: Intention-based reciprocity Incomplete information Hidden costs of control
1. Introduction There is a wide-spread belief in human resource management and the popular business press that exerting control can damage worker performance by eroding motivation and willingness to cooperate.1 This view is consistent with numerous empirical studies from psychology and organizational economics.2 In their prominent study Falk and Kosfeld (2006) investigate such hidden costs of control in an experimental work relationship. Workers can exert costly effort to increase the payoffs of their bosses. Before workers choose effort, bosses decide whether or not to control workers. Imposing control forces workers to exert at least some minimum effort. If workers maximize their own payoffs, they exert the least effort possible to save on effort costs. Falk and Kosfeld find that although many workers indeed always choose the least effort possible, a substantial fraction of workers exert less effort if controlled than if not controlled. Exerting control in fact reduces average effort contributions.3
∗ Correspondence address: Goethe University Frankfurt, Grueneburgplatz 1, 60323 Frankfurt am Main, Germany. Tel.: +49 69 79834815. E-mail address: [email protected] 1 See, for example, Manzoni and Barsoux (1998) and Herzberg (2003) who stress the negative consequences of exerting tight control over employees. Foss (2003) provides a careful case study on the detrimental effects of such micro-management. 2 The extensive empirical literature on monitoring and motivational crowding-out includes Plant and Ryan (1985), Barkema (1995), and Dickinson and Villeval (2008). Further, Enzle and Anderson (1993), Ariely et al. (2008), and Dominguez-Martinez et al. (2010) show that individuals dislike being controlled, and do not dislike being monitored as such. Together these studies document the existence of hidden costs of control. Ryan and Deci (2000) and Frey and Jegen (2001) discuss some theoretical foundations for hidden costs of control, and they provide numerous additional references. 3 Although there is some debate in the literature concerning the magnitude of the effect, an increasing number of studies provide experimental evidence for the existence of hidden costs of control. See in particular Schnedler and Vadovic (2011) and Charness et al. (2012). 0167-2681/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jebo.2013.04.017
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Since choosing high effort remains feasible even when being controlled, such hidden costs of control are incompatible with transitive preferences defined exclusivly over payoff outcomes. Theoretical economic explanations for the observed behavior are therefore almost all based on signaling models.4 However, these explanations can only be relevant if firms have some informational advantage over workers. This is not reasonable in all the circumstances in which there exist hidden costs of control. The present paper complements the existing literature by showing that intentionbased reciprocity can be an alternative explanation for hidden costs of control. This new explanation is not based on signaling. The present analysis further qualifies the wide-spread opinion that intention-based reciprocity is inconsistent with hidden costs of control. At first it might seem very natural to think that workers consider the mere act of not being controlled as kind, and then reciprocate not being controlled with high effort. Yet Falk and Kosfeld (2006, p. 1616) rightly argue that this is inconsistent with existing models of intention-based reciprocity. The reason is that exerting no control has to be considered unkind if uncontrolled workers exert higher effort and thus receive lower payoffs than controlled workers. In other words: if everybody expects workers to always reciprocate not being controlled with particularly high effort, then not exerting control is no longer kind because it reduces the payoff of workers, and thus cannot trigger high effort as reciprocal reaction. The present paper shows that – with a simple extension of the basic model – intention-based reciprocity can explain hidden costs of control. The only requirements are that individuals differ in their propensity for reciprocity, and that preferences are private information.5 After exploring the proposed extension in a more general setup, the model considers a simplified version of the control game from Falk and Kosfeld. The key assumption is that some workers are purely selfish in the sense that they only care for their own monetary payoffs, whereas other workers are reciprocal in the sense of Rabin (1993) and Dufwenberg and Kirchsteiger (2004). They are thus willing to incur some monetary costs to reciprocate kind actions with kind actions. Preferences are private information. The analysis shows that if reciprocal workers are sufficiently reciprocal and the fraction of selfish workers is sufficiently high, there exists a pure-strategy reciprocity equilibrium in which (i) selfish workers always choose the minimum feasible effort, whereas (ii) reciprocal workers choose lower effort if controlled than if not controlled. This equilibrium is based on the following intuition. On the one hand, exerting no control would be unkind if all workers were reciprocal, because then all workers would reciprocate no control with high effort. On the other hand, exerting no control would be kind if all workers were selfish, since then all workers would shirk and consequently get high payoffs. For the existence of the above reciprocity equilibrium, it is thus crucial that workers’ preferences are not only heterogeneous but also private information. In this case bosses do not know their workers’ preferences, and workers know that bosses do not know their workers’ preferences, thus workers must form beliefs concerning the kindness of their bosses’ actions. For this they put themselves into the shoes of their bosses, taking into account only the information that bosses actually have when taking their control decisions. Workers thus derive the average kindness of particular actions. If most workers are rightly expected to be selfish, reciprocal workers might consider it to be on average kind to be left uncontrolled. Reciprocal workers consequently reciprocate not being controlled with high effort. It is important to note that exerting no control is not considered to be kind by reciprocal workers because it provides other selfish colleagues with the opportunity to shirk. Workers have no colleagues in the considered situations. Instead, workers take into account that their bosses rationally believe them to be predominantly selfish! Exerting no control is therefore considered to be kind because (i) it provides also reciprocal workers with the opportunity to get a high payoff by shirking, (ii) this opportunity is not purely hypothetical, since everybody knows that most workers shirk if not controlled, and (iii) bosses do not know workers’ types, and thus risk getting low payoffs by forsaking control. In essence, not controlling workers is kind, exactly because this kindness might not be reciprocated. For illustration of the underlying theoretical mechanism, consider the following example. Suppose a new acquaintance visits your home for dinner. Social convention requires the guest to bring a bottle of wine. Unfortunately, your new acquaintance does not know your preferences concerning white or red wine, and you are aware of this ignorance. It is also commonly known that people typically prefer red wine. But you actually prefer white wine. Would you consider your guest bringing red wine as unkind? The present model would argue that bringing red wine is – given the incomplete information on your preferences and prior beliefs – actually kinder than bringing white wine. This holds even though you actually prefer white wine. The following example further illustrates the importance of incomplete information for the argument. Suppose an employer decides to provide all male workers with a pay rise, while keeping the pay for female workers unchanged. Could this be considered as on average kind by female workers, if the vast majority of employees is male? After all, every worker had a 50% chance of being male at birth. According to the present model, the answer is negative, because gender is observable. Every female worker thus knows that denying a pay rise to female employees is unkind to her, because the employer knows her gender, and therefore knows exactly the unkind consequences of his decision on her pay.
4
The related economics literature is discussed at length in Section 2. The empirical evidence clearly shows that individuals differ in their reciprocal or social preferences. See, for example, Fischbacher and Gächter (2010). Heterogeneity is also an important theoretical component in other model of social preferences. For example, Fehr et al. (2008) and Fehr and Schmidt (2000) show that inequity aversion à la Fehr and Schmidt (1999) is consistent with the laboratory evidence only via the strategic interaction between selfish and inequity averse individuals. 5
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The paper finally illustrates an implicit assumption that follows from the application of existing models of reciprocity, but becomes particularly critical in the presence of incomplete information. This assumption is that reciprocal workers do not dislike selfish workers, and do not use any evaluation of the behavior of selfish workers to assess the kindness of their bosses. Exerting no control is considered to be kind by reciprocal workers, because these workers would also receive a high payoff if they were selfish themselves. But suppose that reciprocal workers would like bosses to punish all selfish behavior, because reciprocal workers also dislike selfish workers. This might imply that reciprocal workers would like bosses to punish them if they were selfish themselves. In that case exerting no control might be considered to be morally wrong, and thus in some sense not deserving high effort as reciprocal response. The implicit assumption in the present specification therefore is that workers should believe that all workers – including themselves – have the right to behave however they want. Consequently, any evaluation of worker behavior does not affect the kindness assigned to the behavior of bosses. 2. Related literature The present analysis adds to the theoretical literature on crowding-out by providing a new rationale for hidden costs of control. In contrast to the present model, all prominent existing explanations are based on signaling. Most closely related are Sliwka (2007) and Ellingsen and Johannesson (2008) who explicitly refer to the control game from Falk and Kosfeld. In Sliwka (2007) bosses signal that there is a high fraction of steadfast fair-minded workers by exerting no control. This induces conformist workers – who want to comply with the prevalent social norm among steadfast workers – to exert high effort. Ellingsen and Johannesson (2008) argue that bosses signal their altruism by exerting no control. This makes it more desirable for workers to signal their altruism. For this signaling to be credible, altruistic workers have to work harder if not controlled than if controlled. These studies complement an extensive signaling literature on motivational crowding-out. The following incomplete list of articles summarizes some of the most popular arguments. In Spier (1992) bosses might leave contracts incomplete – wages do not condition on project outcomes – to signal that the job environment is more likely to yield favorable outcomes. This facilitates worker participation. Bénabou and Tirole (2003) focus on effort choices. Bosses signal that workers’ effort is less productive by opting for strong monetary incentives or control. Although monetary incentives increase motivation in the short run, in the long run the effect is detrimental. In Suvorov and van de Ven (2009) bosses transmit performance information by paying discretionary bonuses. This conveys information on workers’ ability, which in turn affects workers’ future effort decisions. Herold (2010) argues that bosses signal their trust in workers by leaving contracts incomplete. Bosses’ beliefs affect their own effort contributions, which in turn influence workers’ effort choices. In Friebel and Schnedler (2011) bosses signal the intrinsic motivation of some team members by empowering workers. This increases effort by other team members due to complementarities in production. In contrast to all these papers, the present explanation for hidden costs of control is not driven by bosses signaling anything, because in the present context bosses have no private information. The present model can also be distinguished empirically from the signaling explanations of hidden costs of control. Signaling only works if bosses have information that is relevant for workers. This assumption is not always equally plausible. In stable environments experienced workers could have gathered a lot of information on prevalent social norms and the fraction of fair-minded steadfast workers. Experienced workers might also know themselves and their job environment. The altruism of bosses could have been revealed by previous behavior towards other workers and stakeholders. Getting additional information in these situations – via the control choices of bosses – might then have no big impact on beliefs. There should be only limited hidden costs of control. Arguably, also experienced workers react adversely to being controlled. For this case, only the present explanation based on intention-based reciprocity predicts an undiminished deterioration of cooperation.6 The present analysis further complements economic theory on intention-based reciprocity by studying private information on heterogeneous reciprocity concerns. Rabin (1993, p. 1296) argues that “Extending the model to incompleteinformation games is essential for applied research, but doing so will lead to important new issues.” Further, he conjectures that incomplete information might strongly affect results and thus predictions. Geaneakoplos et al. (1989, pp. 67–68) and Battigalli and Dufwenberg (2009) indicate how psychological game theory might encompass private information. The present paper adds to this literature by introducing private information on individual reciprocity concerns. The particular specification is fruitfully applied to a popular research question in organizational economics, and thereby illustrates some of the arising conceptual issues. It corroborates the view that including incomplete information might affect results, since hidden costs of control arise in equilibrium only if reciprocity preferences are private information. Moreover, the study reconciles intention-based reciprocity with the empirical evidence on mutually beneficial conditional cooperation in social dilemmas.7 Such mutually beneficial conditional cooperation is incompatible with the standard intention-based reciprocity model by Rabin (1993), because according to his definition, an action cannot be kind, if it increases
6 However, the present explanation requires that the reciprocity preferences of experienced workers are private information. In the considered situations it must thus be possible to learn the altruism of bosses – because their contract choices are easily observable – whereas it is difficult to learn the reciprocity preferences of workers – because their effort choices are not easily observable. 7 See, for example, Clark and Sefton (2001) on conditional cooperation in a sequential prisoners’ dilemma. They find that extent of conditional cooperation makes it indeed optimal for the first mover to cooperate.
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the equilibrium payoff of everybody, including those taking that action. The reason is that in this case kind and selfish intentions cannot be separated. Rabin’s (1993, pp. 1296–1297) argument is generalized by Netzer and Schmutzler (2012). They show for a large class of games that there cannot be mutually kind behavior in any fairness equilibrium if at least one individual is selfish. This holds because selfish individuals by definition maximize their own payoffs. Their equilibrium actions can therefore be considered at best kindness neutral. The present paper shows that Rabin’s fairness specification can be consistent with profitable conditional cooperation in, for example, the sequential prisoners’ dilemma, if it accounts for private information on heterogeneous reciprocity preferences. The argument runs as follows. There are reciprocal individuals who respond to cooperation with cooperation. Cooperation is kindness neutral towards these individuals if ultimately everyone is better off. But there are also selfish individuals who do not reciprocate cooperative behavior. Cooperation is kind towards these individuals, because it increases their payoffs at the expense of the cooperating individuals. If cooperation is risky – because many individuals are selfish and do not reciprocate – then cooperation might be on average kind, even if it is on average profitable to cooperate. 3. Model This section develops theoretical foundations. Apart from the control game analyzed later, the setup covers many applications that are of interest in organizational economics, including gift exchange and other simple deterministic moral hazard situations. Ignoring incomplete information, the basic strategic situation can be characterized as follows. One boss interacts with one worker. First, the boss chooses some action ab ∈ Ab from a finite set of actions Ab . These actions can be control choices or contract offers. The worker observes the decision of the boss and then decides on his action aw ∈ Aw (ab ) from some finite sets of actions Aw (ab ). These actions could be contract acceptance and effort choices. The sets of feasible actions for the worker might depend on the prior choice of the boss. Monetary payoffs are determined by actions, where b (ab , aw ) is the payoff of the boss and w (ab , aw ) is the payoff of the worker given the actions (ab , aw ). The crucial assumptions in this paper are that (i) workers can differ in their propensity for reciprocity concerns, while (ii) their individual preferences are private information. Workers can be either selfish or reciprocal, so that the type space is = {s, r}. Individual types ∈ are private information, but it is common knowledge that workers are of type with prior probability () ∈]0, 1[. With two types this implies (r) = 1 − (s). Selfish workers are only interested in their own payoff. Reciprocal workers have intention-based fairness concerns in the spirit of Rabin (1993) and Dufwenberg and Kirchsteiger (2004). Market competition arguably forces firms – and thus bosses – to maximize profit. It is thus assumed for simplicity that all bosses are selfish. A working paper version of the present analysis shows that allowing for reciprocal bosses has no substantial impact on the results in the control game studied later.8 Reciprocal workers’ utility is not fully determined by the above payoffs, but also depends on strategies and beliefs concerning strategies. Like the existing literature on intention-based reciprocity, the present paper focuses on pure strategies.9 A fully specified pure strategy for the boss is simply a decision ˛b ∈ Ab . A fully specified strategy for the worker is a function ˛w : × Ab → Aw (ab ) that specifies feasible type-dependent decisions conditional on the observed choices of bosses. Beliefs will also be crucial for the analysis. Define ˇw as the belief of bosses concerning the strategy of workers, and let w be the belief of workers concerning the belief of bosses concerning the strategy of workers. Further, denotes the probabilities with which bosses believe to be facing workers with certain types, and describes the belief of workers concerning the probabilities with which bosses believe to be facing workers with certain types. 3.1. Kindness with incomplete information on workers’ reciprocity The present paper applies the definitions of reciprocity by Rabin (1993) and Dufwenberg and Kirchsteiger (2004) while accounting for incomplete information on workers’ reciprocity preferences.10 As with complete information, the kindness of an action is assessed by putting the payoff consequences of that action in relation to the set of payoff consequences that could have been achieved via alternative actions. Incomplete information comes into the picture since the same action can have different payoff consequences for selfish and reciprocal workers.
8 See von Siemens (2011). The only difference to the present study is that reciprocal bosses’ control choices are influenced by their fairness concerns. This can explain heterogeneous control choices even though in equilibrium all bosses and workers share the same consistent beliefs concerning workers’ equilibrium behavior. 9 It is not trivial to evaluate the kindness of an observed action resulting from a mixed strategy, as it could depend on whether mixed strategies are viewed as deliberate mixing by an individual or as a description of the behavior of a population with heterogeneous individuals using different pure strategies. For some theory and experimental evidence on this complicated matter see Aldashev et al. (2010). Further, the intentions of any observed actions will be interpreted as if behavior was always fully deliberate. This seems more appropriate in the context of pure strategies. For further discussion, see Rabin (1993, p. 1286), Dufwenberg and Kirchsteiger (2004, p. 275 and pp. 279–280), and Segal and Sobel (2007, pp. 209–210). 10 Results are largely indifferent to the exact specification of reciprocity preferences. In particular, it does not really matter whether the definition of kindness follows Rabin (1993) and Dufwenberg and Kirchsteiger (2004). A discussion of the implications of different reciprocity concepts is thus deferred to Section 5.
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Consider first the kindness of workers’ actions towards bosses who have chosen some arbitrary action ab ∈ Ab . Let ˘ b (ab ) ˜ b (ab ) be be the set of payoff combinations that workers can then implement by choosing some actions aw ∈ Aw (ab ). Let ˘ the Pareto-efficient frontier of this set of payoff combinations. Let bh (ab ) and b (ab ) be the highest and lowest payoffs
for bosses from this set of Pareto-efficient payoff combinations. Define be (ab ) = (bh (ab ) + b (ab ))/2 as the equitable payoff. This equitable payoff characterizes the kindness-neutral payoff benchmark.11 Let bmin (ab ) be the minimum payoff for bosses from the set ˘ b (ab ). Note that this minimum payoff might originate from a Pareto-dominated payoff combination. Then kwb (ab , aw ) =
b (ab , aw ) − be (ab ) bh (ab ) − bmin (ab )
(1)
is the kindness of workers with action aw towards bosses with action ab . This definition applies whenever the denominator is not equal to zero. Otherwise, workers cannot influence bosses’ payoffs, and all actions are assigned a kindness of zero. The kindness of workers’ actions depends on the set of feasible payoff combinations and thus on bosses’ actions. Moreover, beliefs about strategies are irrelevant since workers know exactly the payoff consequences of their actions. Consider next the kindness of certain actions chosen by bosses. To simplify the exposition, first assume that it is common knowledge that workers follow strategy ˛w while fraction () of workers has preferences ∈ . As in Dufwenberg and Kirchsteiger (2004) any choices by bosses are considered to be fully intentional. The kindness of bosses’ actions then depends on the resulting payoffs for workers. Reciprocal and selfish workers might respond differently to the same control choices. Further, bosses cannot know their workers’ types, and this is common knowledge among bosses and workers. This poses the question of how to include incomplete information on workers’ preferences in a model with intentionbased reciprocity. The main idea is that the kindness of an action is determined by the information available to the individuals taking that action. Workers thus first derive the kindness of an action separately towards workers with selfish and reciprocal preferences, that is, towards workers with particular action responses. They then compute the sum of the type-dependent kindnesses towards selfish and reciprocal workers, weighted with the respective probabilities with which bosses believe to be facing these types of workers. Workers simply form the expected kindness of an action.12 This idea is reflected in the formal definitions as follows. Given that workers employ strategy ˛w define ˘w (˛w , ) as the set of payoff combinations that bosses can implement when paired with workers of type ∈ by choosing actions ˜ w (˛w , ). The resulting payoffs h (˛w , ), (˛w , ), ab ∈ Ab . This set of payoff combinations has Pareto-efficient frontier ˘ w w e (˛ , ), and min (˛ , ) are defined analogously to the above definitions. Then w w w w kbw (ab , ˛w , ) =
e (˛ , ) w (ab , ˛w (, ab )) − w w h (˛ , ) − min (˛ , ) w w w w
(2)
is the kindness of action ab towards workers with type if workers employ strategy ˛w . The kindness of an action ab is normalized to zero whenever the denominator is zero. Given workers’ strategy ˛w it is possible to compute the kindness of an action ab towards all types of workers ∈ . Then
() kbw (ab , ˛w , )
(3)
∈
is the expected kindness of bosses choosing action ab . Following Rabin (1993) and Dufwenberg and Kirchsteiger (2004), the kindness of an action thus follows from equilibrium payoff consequences. The definition does not take into account that reciprocating an unkind action might create utility in itself, for example, by arousing strong spiteful emotions. Otherwise, being unkind might turn out to be kind, if the resulting spiteful emotions are sufficiently strong. Moreover, the kindness of an action does not depend on the payoffs that workers could have obtained by deviating from their equilibrium strategy. This is driven by the idea that in equilibrium individuals should hold expectations that are consistent with equilibrium behavior. Segal and Sobel (2007) propose another definition of reciprocity that accounts for payoffs that can only be obtained off equilibrium. The difference between the present and their approach is further discussed in Section 5. The above definitions are based on the assumption that it is common knowledge that workers employ strategy ˛w and are of type ∈ with probability (). If bosses assess the kindness of their own actions, then in general their assessment depends on their belief ˇw concerning the strategy of workers, and on the probabilities with which they believe workers to be of certain types. If workers assess the kindness of actions taken by bosses, then in general their assessment depends on
11 Due to the restriction to Pareto-efficient payoff combinations, an action that increases payoffs for everybody must be assessed as kindness-neutral. Exactly this definition makes it impossible in the basic model by Rabin to explain mutually beneficial cooperation as equilibrium phenomenon in social dilemmas. 12 An alternative approach would be to treat type-dependent pure strategies as if worker were using mixed strategies. In the control game studied later, exerting no control can then be assessed as kind if it provides workers with higher and bosses with lower expected payoffs than exerting control. Mutually profitable conditional cooperation is no longer possible, see the discussion in the introduction. Otherwise, results are largely robust to this alternative specification. However, viewing individuals as using mixed strategies only seems plausible if in equilibrium individuals are almost indifferent between the relevant actions. In the control game studied later this need not be the case with selfish and reciprocal individuals, since the reciprocal action might result in substantially lower monetary payoffs than the selfish action.
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their belief w concerning the belief of bosses concerning the strategy of workers, and on the beliefs with which workers believe bosses to believe workers to be of certain types. The more general definition of kindness then follows from the above, where ˛w and in (2) and (3) are replaced with the corresponding first-order and second-order beliefs. 3.2. Preferences Given action ab and the involved beliefs and ˇw define Ub (ab , ˇw , ) =
() b (ab , ˇw (, ab ))
(4)
∈
as the expected utility of bosses. Bosses simply care for their expected monetary payoff. The utility of workers given their action aw , action ab by their bosses, and beliefs w and concerning the beliefs of bosses, is defined as Uw (aw , ab , w , ) = w (ab , aw ) + () kwb (ab , aw )
() kbw (ab , w , )
(5)
∈
where () ∈ IR+ characterizes the relative importance of reciprocity concerns for workers with type ∈ . It is assumed that
(r) > (s) = 0. Reciprocal workers thus care for their own expected payoffs, but they also care for fairness. Selfish workers only care for their own expected payoffs. Bosses and workers maximize expected utility. 3.3. Reciprocity equilibrium The equilibrium notions of Rabin (1993) and Dufwenberg and Kirchsteiger (2004) are adapted to the present context with incomplete information as follows. ∗ , ˛∗ , ∗ , ∗ , ∗ ) is characterized by Definition 1 (Reciprocity equilibrium). A reciprocity equilibrium (˛∗b , ˇw w w
˛∗b
∈ argmax a∈Ab
∗
∗ () b (a, ˇw (, a))
,
˛∗w (, ab )
(6)
∈
∈ arg max
a∈Aw (ab )
w (ab , a) + () kwb (ab , a)
∗
∗ () kbw (ab , w , )
(7)
∈
∗ = ∗ , * = * = . for all ∈ and ab ∈ Ab , and ˛∗w = ˇw w
First, equilibrium strategies maximize expected utility given all equilibrium strategies, given bosses’ equilibrium firstorder beliefs, and given workers’ equilibrium second-order beliefs. Second, first-order and second-order beliefs are consistent with prior beliefs and equilibrium strategies. Thirdly, the above holds at all decision nodes – that is after seeing any initial choice by bosses. This implies that equilibria cannot be based on unreasonable behavior off the equilibrium path. Fourthly, the definitions imply that the kindness of actions is assessed under the assumption that any observed actions are fully intentional. 4. Control game The remainder of the paper applies the developed general concept to study hidden costs of control. The strategic situation is as follows. First, the boss decides whether or not to control the worker, ab ∈ Ab = {c, nc}. Control is costless. The worker observes the decision of the boss and then decides on his effort aw . Effort can be high, medium, or low. The set of possible effort choices Aw (ab ) depends on the control decision ab of the boss, where Aw (c) = {h, m} and Aw (nc) = {h, m, }. By controlling the worker, the boss can thus prevent the worker from exerting low effort. The worker’s effort choice determines both his payoff and the payoff of the boss via the payoff functions b : Aw → IR and w : Aw → IR. More effort strictly increases the payoff of the boss and strictly decreases the payoff of the worker, thus b (h) > b (m) > b ( ) and w ( ) > w (m) > w (h). The sequence of actions is summarized in Fig. 1. All bosses are selfish, whereas workers are either selfish or reciprocal. A fully specified pure strategy for bosses is a control choice ˛b ∈ Ab . A fully specified strategy for workers is a function ˛w : × Ab → Aw (ab ) that specifies type-dependent effort choices conditional on bosses’ control choices. To avoid tedious and uninformative case distinctions, the following cutoff rule is implemented in the equilibrium analysis of the control game: in case of indifference workers choose the lower effort, and bosses control their workers. This makes it harder to achieve the goal of the study – to find an equilibrium in which some bosses do not control while reciprocal workers reciprocate not being controlled with exerting high effort.
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Fig. 1. Control game.
4.1. Hidden costs of control This section derives the existence conditions for a reciprocity equilibrium in which reciprocal workers reciprocate not being controlled by exerting high effort. Since the kindness of workers towards bosses does not depend on any beliefs or types, (1) implies the following in any equilibrium. Lemma 1 (Kindness of worker). In any reciprocity equilibrium 1 kwb (c, m) = − ; 2
kwb (c, h) = +
1 2
1 kwb (nc, ) = − ; 2
kwb (nc, m) =
(8)
and 2 b (m) − b (h) − b ( ) ; 2(b (h) − b ( ))
kwb (nc, h) = +
1 2
(9)
characterize the kindness of workers towards bosses. A selfish worker always maximizes his payoff, and therefore chooses the minimum possible effort. This directly implies the following. Lemma 2 (Behavior selfish workers). In any reciprocity equilibrium ˛∗w (s, nc) = and
˛∗w (s, c) = m
(10)
characterize the equilibrium behavior of selfish workers. max (˛∗ , s) = ( ), Since the behavior of selfish workers is identical in all equilibria, Lemma 2 yields directly w w w min (˛∗ , s) = (m), and e (˛∗ , s) = ( ( ) + (m))/2. This implies that controlling a selfish worker is unkind, whereas w w w w w w w not controlling a selfish worker is kind.
Lemma 3 (Kindness of bosses towards selfish workers). In any reciprocity equilibrium kbw (nc, ˛∗w , s) = +
1 2
and
kbw (c, ˛∗w , s) = −
1 2
(11)
characterize the kindness of bosses towards selfish workers. Before presenting the main result define
˜1 =
w ( ) − w (h) 1 − 2
(12)
˜2 =
2(w (m) − w (h))(b (h) − b ( )) . (1 − 2)(b (h) − b (m))
(13)
and
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Further, define ˜ = b (m) − b ( ) . b (h) − b ( )
(14)
The main result is made formally precise in the following proposition. Proposition 1 (High effort reciprocation). Consider a reciprocity equilibrium in which reciprocal workers reciprocate not being controlled so that ˛∗w (r, nc) = h and ˛∗w (r, c) = m. Selfish workers behave as characterized in Lemma 2. Then the following holds. 1 Such an equilibrium exists if and only if (r) < 1/2 and (r) > max{
˜ 1,
˜ 2 }. ˜ 2 Bosses choose control if and only if (r) ≤ . max (˛∗ , r) = (m) and min (˛∗ , r) = (h) so that e (˛∗ , r) = ( (m) + Proof. Workers’ equilibrium behavior yields w w w w w w w w w w (h))/2. Concerning the kindness of bosses towards reciprocal workers this yields kbw (nc, ˛∗w , r) = −1/2 and kbw (c, ˛∗w , r) = 1/2. The expected kindness of bosses towards workers with unknown type is then
()kbw (c, ˛∗w , ) = (r) − 1/2 and
∈
()kbw (nc, ˛∗w , ) = 1/2 − (r).
(15)
∈
Consider the optimality of the equilibrium behavior of bosses and workers. Consider first workers. The behavior of selfish workers is optimal given Lemma 2. Given the cutoff rule the behavior of reciprocal workers is optimal if and only if w (h) + (r)
w (h) + (r)
1 2
1 2
1
− (r)
1
− (r)
w (m) − (r) (r) −
2
1 2
2
> w ( ) − (r)
2
> w (m) + (r)
1 2
1
1
2
1
− (r)
(16)
2
2 (m) − (h) − ( ) b b b
− (r)
≥ w (h) + (r) (r) −
1 2
2(b (h) − b ( ))
1 2
.
(17)
(18)
Constraints (16) and (17) ensure that if not controlled, reciprocal worker prefer to exert high rather than medium or low effort. (18) ensures that if controlled, reciprocal workers prefer to exert medium rather than high effort. As w (h) < w ( ) constraint (16) can hold only if (r) < 1/2. This condition with w (m) > w (h) implies that (18) can be ignored. Rearranging (16) yields as condition (r) >
˜ 1 and rearranging (17) yields (r) >
˜ 2 . Note that since b (h) − b ( ) > b (h) − b (m) it is not clear whether (16) or (17) is binding even though w ( ) − w (h) > w (m) − w (h). Consider next the optimality of the equilibrium behavior of bosses. The condition on (r) simply follows from comparing expected payoffs when controlling and not controlling. The intuition for this result is as follows. If workers are selfish with high probability – the ex ante probability (r) to be reciprocal is smaller than 1/2 – then controlling workers with unknown type is on average unkind, whereas not controlling workers with unknown type is on average kind. If reciprocal workers sufficiently care for reciprocity – the reciprocity parameter (r) exceeds a certain threshold – then they reciprocate not being controlled by exerting high effort. Note that the exact cutoff values for (r) and (r) clearly depend on the specification of reciprocity preferences. With an alternative specification like Falk and Fischbacher (2006) there might exist similar equilibria even if the majority of workers are reciprocal. The same holds true if the kindness of an action is not normalized as in Rabin (1993) but depends on absolute payoff differences as in Dufwenberg and Kirchsteiger (2004). Further, in equilibrium it can be optimal for bosses to exert control although reciprocal workers would exert high effort if they were not controlled. Such an equilibrium exists if and ˜ 1/2}. Exerting no control then does not pay, either because too few workers are reciprocal, or because only if (r) ≤ min{, exerting high rather than medium effort does not increase payoffs sufficiently. The reciprocity equilibrium as characterized in Proposition 1 exhibits the most important qualitative features of hidden costs of control as observed in the empirical studies. In contrast to all prominent theoretical explanations for hidden costs of control, signaling cannot play any role, because bosses possess no private information. 4.2. All other pure-strategy reciprocity equilibria This section shows that in the present context there exist only rather intuitive reciprocity equilibria in pure strategies. The focus is on the intuition; all technical details are available upon request. Proposition 1 describes the reciprocity equilibrium for high levels of reciprocity. For medium levels of reciprocity there exists a reciprocity equilibrium in which reciprocal workers always exert medium effort. Not exerting control is then kind to selfish workers, and kindness neutral to reciprocal workers. Reciprocity concerns have to be sufficiently strong such that reciprocal workers do not exert low effort if they are not controlled, but they must also be sufficiently weak such that reciprocal workers do not exert high effort if they are not controlled. Bosses always control since not controlling never
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increases effort, not even for reciprocal workers. For low levels of reciprocity, there exists a reciprocity equilibrium in which reciprocal and selfish workers behave in the same way: they always choose the least effort possible. Not controlling is kind to all types of workers. However, reciprocity concerns are weak so that even unambiguously kind actions cannot trigger effort choices that exceed low effort. Bosses control because this increases effort contributions from both selfish and reciprocal workers. There exist no other reciprocity equilibria in pure strategies. The reason is that in any other equilibrium reciprocal workers would have to exert high effort once controlled. This can only be optimal if controlling workers is considered to be kind. The latter is never the case for selfish workers. It also cannot be kind to reciprocal workers for the following reason. Reciprocal workers cannot exert more than high effort if they are not controlled. Thus, exerting control is at most kindness neutral towards reciprocal workers. But then reciprocal workers maximize their payoffs and do not exert more than the minimum effort. This demonstrates that the theory possesses predictive power: reciprocal workers never exert more than the least effort possible if they are controlled. 5. Further related literature This section discusses some aspects of the current model specification by connecting results to further related literature. Particularly, it shows that the main result – in equilibrium some workers might respond to control by lowering their effort – is quite robust with respect to the exact specification of reciprocity preferences. In contrast to the present specification, Falk and Fischbacher (2006) assume that reciprocity preferences are influenced by payoff inequality. Workers consider a control choice as kind if and only if they consequently receive higher payoffs than their bosses. The following argument demonstrates that using this definition of reciprocity does not change results fundamentally. Suppose reciprocal workers reciprocate not being controlled with high effort. Reciprocal workers consider not being controlled as kind if the resulting payoff difference w (h) − b (h) is positive. But since in equilibrium they then exert only medium effort, being controlled is even kinder to reciprocal workers. The reason is that the payoff difference w (m) − b (m) exceeds w (h) − b (h). Further, since w (h) is the minimum payoff bosses can grant workers in equilibrium, the kindness of choosing no control is further reduced to capture intentions. As the present specification, Falk and Fischbacher (2006) thus imply that exerting no control is less kind towards reciprocal workers than exerting control. However, selfish workers choose low effort if not controlled and medium effort if controlled. Towards selfish workers exerting no control is kinder than exerting control. If the kindness of bosses is the weighted sum of the kindness of bosses towards selfish and reciprocal workers, then exerting no control can be considered as kind, if and only if the fraction of reciprocal workers (r) is below some cutoff. The present equilibrium arguments then apply. The only major difference is that the cutoff for (r) depends on payoffs and can differ from 1/2. There might thus exist an equilibrium in which a majority of workers exert high effort when not being controlled. Segal and Sobel (2007, pp. 206–209) take a rather different approach towards reciprocity. They argue that the kindness of a control choice depends on the resulting maximum feasible payoff for workers. This definition implies that no control is kinder than control, because only no control allows workers to get the highest payoff by shirking. But with homogeneous workers this definition of kindness – kindness depends on what workers could do, but not an what they actually do – implies that a control choice can be kind even if the subsequent equilibrium result is unfavorable for workers. With heterogeneous reciprocity concerns, there exist selfish workers that in equilibrium do abuse every opportunity to maximize their own payoffs. Allowing for private information on heterogeneous reciprocity concerns thus in some sense reconciles the definitions of kindness from Rabin (1993) and Segal and Sobel (2007). The only remaining difference to Segal and Sobel (2007) is that the fraction of selfish workers influences the kindness of bosses’ control choices. Schnedler and Vadovic (2011) sketch how hidden costs of control might be caused by guilt aversion in the spirit of Battigalli and Dufwenberg (2007). Bosses could expect – because of social norms or the framing of the decision environment – that workers exert less effort if controlled than if not controlled. Guilt averse workers match these expectations, so that behavior and expectations are consistent in equilibrium. However, in such models of guilt aversion it seems to be a priori unclear what might constitute reasonable expectations. In particular, there might also exist an equilibrium in which bosses rightly expect workers to exert higher effort if controlled than if not controlled. Rabin (1993, p. 1285) argues that one advantage of intention-based reciprocity is that it derives all behavioral components – the psychological game – from the material payoffs of the underlying strategic interaction. Section 4.2 shows that this approach rules out unreasonable equilibria. The present analysis thus demonstrates that despite restrictions on reasonable equilibrium behavior, intention-based reciprocity might well explain hidden costs of control if there is incomplete information on individual reciprocity preferences. 6. Conclusion The present paper shows that intention-based reciprocity can explain hidden costs of control if individuals differ in their propensity for reciprocity concerns while preferences are private information. This complements the existing theoretical literature by offering an explanation for hidden costs of control that is not based on signaling. The present study also extends existing models of intention-based reciprocity by introducing private information on heterogeneous reciprocity concerns. It demonstrates that this extension generates new predictions that are consistent with the empirical evidence on profitable conditional cooperation. Unobservable heterogeneity seems to be very plausible in most economic situations – including
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all laboratory experiments. This creates ample scope to further explore the extended explanatory power of intention-based reciprocity in future applications. Finally, the analysis complements a recent strand of papers that apply models of reciprocity, conditional altruism, and conditional cooperation. von Siemens (2009) shows how reciprocity can improve investment incentives in a hold-up situation. I˙ ris¸ and Santos-Pinto (2013) derive conditions under which reciprocity among managers facilitates or complicates collusion in the product market. Dur et al. (2010) and Dur and Sol (2010) investigate optimal incentive contracts if workers reciprocate the attention of managers or colleagues by exerting more effort. Netzer and Schmutzler (2012), Non (2012), and Englmaier and Leider (2013) study optimal monetary incentives if workers reciprocate overly generous employment contracts with higher effort. Non (2012) accounts for heterogeneous reciprocity concerns among workers, but builds his analysis on type-based reciprocity by Levine (1998) and not on intention-based reciprocity by Rabin (1993). Kosfeld and von Siemens (2009, 2011) show how firms can use incentive contracts to promote conditional cooperation among workers through worker selection. Finally, Sebald (2010) and Aldashev et al. (2010) argue that reciprocity concerns can influence not only optimal wage contracts but also appointment procedures. But none of these papers studies hidden costs of control as in Falk and Kosfeld (2006), and none of them investigates the impact of private information on heterogeneous reciprocity concerns in a model with intention-based reciprocity. Proponents of outcome-based social preferences often argue that theories of intention-based reciprocity suffer from serious drawbacks that include multiple – often counterintuitive – equilibria and a high degree of complexity. The present paper shows that these arguments are justified: applying reciprocity even in simple strategic situations raises substantial conceptual complications. But the present also demonstrates that these problems can be overcome. The application of intention-based reciprocity to economic problems – especially when outcome-based fairness concerns cannot explain the empirical evidence – might thus offer a fruitful avenue for future investigation. Acknowledgements Very helpful comments and suggestions from Josse Delfgaauw, Georg Kirchsteiger, Jurjen Kamphorst, Michael Kosfeld, Matthew Rabin, Wendelin Schnedler, Alexander Sebald, Randolph Sloof, Joep Sonnemans, Jeroen van de Ven, and two anonymous referees are gratefully acknowledged. References Aldashev, G., Kirchsteiger, G., Sebald, A., 2010. How (not) to decide: procedural games. ECORE Discussion Paper 2010/81. Ariely, D., Kamenica, E., Prelec, D., 2008. Man’s search for meaning: the case of legos. 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