Being of two minds: Ultimatum offers under cognitive constraints

Journal of Economic Psychology 32 (2011) 940–950

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Being of two minds: Ultimatum offers under cognitive constraints Dominique Cappelletti a,⇑, Werner Güth b, Matteo Ploner a,c a b c

Computable and Experimental Economics Laboratory (CEEL), University of Trento, Via Inama 5, 38122 Trento, Italy Max Planck Institute of Economics, Strategic Interaction Group, Kahlaische Strasse 10, 07745 Jena, Germany Department of Economics, University of Trento, Via Inama 5, 38122 Trento, Italy

a r t i c l e

i n f o

Article history: Received 20 July 2010 Received in revised form 2 August 2011 Accepted 3 August 2011 Available online 10 August 2011 JEL classification: C72 C78 C91

a b s t r a c t We experimentally investigate how proposers in the Ultimatum Game behave when their cognitive resources are constrained by time pressure and cognitive load. In a dual-system perspective, when proposers are cognitively constrained and thus their deliberative capacity is reduced, their offers are more likely to be influenced by spontaneous affective reactions. We find that under time pressure proposers make higher offers. This increase appears not to be explained by more reliance on an equality heuristic. Analysing the behaviour of the same individual in both roles leads us to favour the strategic over the otherregarding explanation for the observed increase in offers. In contrast, proposers who are under cognitive load do not behave differently from proposers who are not. Ó 2011 Elsevier B.V. All rights reserved.

PsycINFO classification: 2340 2360 Keywords: Ultimatum Game Dual-system theories Time pressure Cognitive load Experimental economics

1. Introduction The influence of affect on economic decisions has been investigated in a variety of contexts. In ultimatum bargaining, negative affective states have been shown to be an important motivating factor behind rejection of unfair offers (e.g., Pillutla & Murnighan, 1996; Sanfey, Rilling, Aronson, Nystrom, & Cohen, 2003; vant´ Wout, Kahn, Sanfey, & Aleman, 2006). This is particularly the case when negative affective states are not controlled or alleviated. Indeed, their effect on rejection behaviour is greatly reduced when, for example, responders can alleviate them by expressing their feelings directly to proposers (Xiao & Houser, 2005) or by delaying the acceptance decision (Grimm & Mengel, 2011). While extensive research has been conducted on the affective aspects of responder behaviour, the affective influences on proposer behaviour have been almost entirely disregarded. A possible reason for this neglect is of methodological nature. While, in the case of responders, affect resulting from the receipt of an offer can be examined through self-reported and physiological measures, or through the measurement of activity in the brain areas associated with it, in the case of proposers there is not an event or a stimulus ⇑ Corresponding author. Tel.: +39 0461282312. E-mail address: [email protected] (D. Cappelletti). 0167-4870/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.joep.2011.08.001

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to react to. In this paper we investigate the influence of affect on proposer behaviour in the Ultimatum Game1 by using a dual-system approach to decision-making. This approach assumes that decision-making is governed by the interplay of an instinctive affective system and a controlled deliberative system and that cognitive resources are needed for both implementing deliberative processes and overriding affective processes (e.g., Kahneman, 2003; Loewenstein & O’Donoghue, 2007). Thus, constraining cognitive resources has the consequence to enhance the influence of affect on behaviour. Specifically, we constrain cognitive resources by imposing time pressure and cognitive load on proposers. Our results show that proposers offer more under time pressure. This increase is not explained by more reliance on an equality heuristic. Comparing offers made and acceptance thresholds of proposers, who were asked what they would accept as a responder, leads us to favour the strategic over the other-regarding explanation for the observed increase in offers. Interestingly, our research shows that proposer offers appear to be unaffected by cognitive load manipulation. The remainder of the paper is organized as follows: the next two subsections review some related work and outline the behavioural predictions; Section 2 describes the experimental design and procedures; Section 3 presents the results and discusses the findings; Section 4 concludes. 1.1. Dual-system approach to decision-making The idea that human thinking and decision-making are governed by two different but interacting systems has been increasingly recognized as influential in psychology (Epstein, 1994; Kahneman, 2003; Lieberman, 2003, chap. 3; Metcalfe & Mischel, 1999; Sloman, 1996; Stanovich, 1999). Recently, a number of dual-process models have been proposed also in economics, with applications to intertemporal choice, labour supply, risk preferences, and social preferences (Benhabib & Bisin, 2005; Bernheim & Rangel, 2004; Fudenberg & Levine, 2006; Loewenstein & O’Donoghue, 2007). These models, mostly known as ‘‘dual-self models’’ in economics, view economic behaviour as determined by the interaction between two different systems, an affective and a deliberative system. The affective system is fast, automatic, minimally demanding of cognitive resources, myopic, and primarily driven by affective states, while the deliberative system is slow, affect free, maximally demanding of cognitive resources, deliberately controlled, goal-oriented, and forward-looking. This dual-system view is also supported at a neural level. Recent neuroimaging evidence indicates that affective and deliberative processes share some common neural components, but activate distinct neural areas. Deliberative processes are associated with the outer part of the brain (neocortex), in particular with anterior and dorsolateral regions of prefrontal cortex, while affective processes are associated with the inner part of the brain (the limbic system), which includes anterior and posterior cingulate cortex, insular cortex, orbitofrontal cortex, and the amygdala (Cohen, 2005; Dolan, 2002; Sanfey, Loewenstein, McClure, & Cohen, 2006). An important implication of these dual-system models of decision-making is that the two systems can have conflicting motivations, and behaviour depends on which of the two systems prevails. For example, in a neuroimaging study of intertemporal choice, McClure, Laibson, Loewenstein, and Cohen (2004) found that the limbic system is particularly activated when the decision involves an immediate reward, while neocortical regions associated with deliberative processes remain unvaryingly activated in all decisions. Moreover, choices are predicted by the relative level of activation of the two systems. Affect is likely to have a larger influence on decision-making either when the affective system is stimulated or when the deliberative system is weakened. It has to be noted that the deliberative system plays a role in self-regulation, including emotion regulation (e.g., Ochsner & Gross, 2005). Therefore, when it is weak, it is not only less involved in the decision-making process, but also loses control of the affective system. The affective system can be stimulated in different ways, for example by manipulating the temporal, spatial, and social proximity of environmental stimuli (e.g., Ditto, Pizarro, Epstein, Jacobson, & MacDonald, 2006; Loewenstein, 1996). The deliberative system is weakened by all those factors, such as time pressure, cognitive load, and mental depletion, that tax the processing resources on which it relies (Lobel & Loewenstein, 2005). Time pressure weakens the role of the deliberative system in decision-making mainly in two ways.2 First, since deliberation takes time, a shortage of time tends to reduce deliberative processing. Second, when it is constrained, time needs to be monitored. This activity absorbs a part of central processing resources (Zakay, 1993, chap. 4), crowding out deliberation and self-regulation. In an Ultimatum Game experiment, Sutter, Kocher, and Strau (2003) showed that time pressure leads responders to bargain more aggressively, driving up the number of rejections. Cognitive load impedes deliberative processing because scarce resources must be allocated to different simultaneous tasks. In addition, less resources are available for self-regulation. Cognitive load is usually manipulated through a dual-task procedure in which subjects have to complete another task while performing the task of primary interest. Frequently used secondary tasks include memory tasks and vocal or manual reaction-time tasks. Previous studies showed that people under 1 The Ultimatum Game is a two-party game in which one party (the proposer) makes an offer to the other party (the responder) about how to split a sum of money between them. If the offer is accepted, the sum of money is split as agreed. If the offer is rejected, both players earn nothing. The game theoretic solution predicts that the responder accepts any amount greater than zero and, thus, the proposer offers the smallest possible amount. However, decades of experimental research have reported that both the proposer and the responder behave in a way that is inconsistent with the theory. On average, proposers offer about 30–40% of the endowment, with 40–50% being the modal offer. On the other side, responders reject offers of less than 20% of the endowment about half the time (for a review, see Camerer, 2003). 2 Some researchers emphasize the effect of time pressure on the affective system, showing how time pressure may increase the level of arousal (for example, see Maule & Hockey, 1993, chap. 6).

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higher cognitive load are more likely to choose an affect-laden option (Shiv & Fedorikhin, 1999), become more impatient (Hinson, Jameson, & Whitney, 2003), offer more in the Dictator Game if they are prosocials (Cornelissen, Dewitte, & Warlop, 2011), and are more likely to request an equal amount from a common resource pool (Roch, Lane, Samuelson, Allison, & Dent, 2000). Finally, a variety of factors, such as stress, exhaustion, sleep deprivation, and decision fatigue contribute to the depletion of mental resources and thus reduce the resources available for decision-making and self-regulation. Previous studies showed that making a series of choices in an effortful, deliberate manner impairs the subsequent exertion of self-control (Vohs et al., 2008) and increases attraction to affective aspects of products (Bruyneel, Dewitte, Vohs, & Warlop, 2006). In an Ultimatum Game experiment, Anderson and Dickinson (2010) showed that sleep deprivation leads responders to behave more aggressively, rejecting unequal-split offers at a higher rate. This study investigates the impact of spontaneous affective reactions on proposer offers in the Ultimatum Game (Güth, Schmittberger, & Schwarze, 1982). Using a dual-system approach, we try to inhibit deliberative processing by imposing cognitive load and time pressure on proposers, so that they are more vulnerable to the influence of the affective system. The next section outlines our behavioural predictions. 1.2. Behavioural predictions Predicting how proposers behave when their cognitive resources are constrained is not straightforward. Ultimatum offers may be driven by two components: fear of rejection (strategic component) and other-regarding concerns. Strategic considerations lead a proposer to make an offer that is at least equal to the minimum offer that she expects to be accepted by the responder. Offering more than the expected minimum acceptable offer can be attributed to other-regarding concerns. Strategic considerations require time and cognitive resources. If these are constrained, proposers may be more likely to engage in a relatively effortless heuristic reasoning that leads them to choose the salient equitable split. If this is the case, we should observe a significant increase in the frequency of equal-split offers when cognitive capacity is limited. About the other-regarding component, two approaches have been suggested. According to the intuitionist approach (Haidt, 2001), moral decisions are primarily driven by quick, automatic, effortless affective processes. According to van Winden (2007), ‘‘it is probably not so much cognition but emotion that plays a major role in the individual enforcement of, as well as the compliance with, norms like fairness’’ (p. 50). The findings of Roch et al. (2000) and Cornelissen et al. (2011) reported above are in line with the intuitionist hypothesis. In addition, assuming that instinctive responses result in less response time than cognitive responses, Rubinstein (2007) found that equal division is the more instinctive choice in the Ultimatum Game. Following the intuitionist approach, inhibiting deliberative processing should increase other-regarding concerns. In contrast, the rationalist approach views moral decisions as resulting from reasoning and reflection. As Moore and Loewenstein (2004) maintain, self-interest is automatic, unconscious, and viscerally compelling, whereas considering others generally requires thoughtful processing. The results reported by van den Bos, Peters, Bobocel, and Ybema (2006), Knoch, Pascual-Leone, Meyer, Treyer, and Fehr (2006) and Piovesan and Wengström (2009) support the rationalist hypothesis. In van den Bos et al.’s (2006) experiments, subjects are more satisfied with advantageous unequal outcomes when their cognitive processing is limited (through either a cognitive-load or a time-pressure manipulation). Knoch et al. (2006) found that the disruption of the right dorsolateral prefrontal cortex, a brain area associated with deliberative processes, increases the acceptance rate of unfair ultimatum offers.3 In a study of response times in a modified Dictator Game, Piovesan and Wengström (2009) found that faster dictators make egoistic choices more often than slower dictators. Following this approach, inhibiting deliberative processing should reduce other-regarding concerns. One might expect the intuitionist approach to find support in our experiment: since previous studies generally showed that the affective system strengthens fairness concerns in responders, it is plausible that it has the same effect on proposers’ behaviour. However, it has to be noticed that the decision faced by proposers and that faced by responders are inherently different: the responder’s decision is simply a choice between accepting and rejecting an offer and misses the strategic component that characterizes the proposer’s decision. Therefore, it might be that the additional strategic component generates different affective reactions and decision outcomes of proposers and responders.4 We tested these predictions experimentally. Our experimental design and procedures are detailed in the next section. 2. Method 2.1. Treatments The experiment has a 2 (cognitive load: load vs. no load)  2 (time pressure: high vs. low)  2 (incentives: low vs. high) between-subject design. The eight treatments are summarized in Table A.1. 3 However, subjects’ fairness judgments are not influenced by this manipulation, indicating that this area of the brain is crucial for the implementation of fairness-related responses. 4 A different weight of fairness considerations in proposer’s and responder’s behaviour has been also documented by Schotter and Sopher (2007). In a study on the impact of advice on ultimatum behaviour, they found that fairness arguments are often used to justify responder behaviour, but hardly used to justify proposer behaviour.

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Cognitive load was manipulated through a dual-task procedure. Participants in the cognitive-load condition (cl1) were asked to memorize five 3-digit numbers and keep them in mind while deciding in an Ultimatum Game (hereafter UG). In contrast, participants in the no cognitive-load condition (cl0) did not confront the memory task while deciding in the UG. Time pressure was manipulated by setting a time limit for deciding in the UG. Participants in the high time-pressure condition (tp1) had 15 s to decide as proposers and 30 s to decide as responders. The difference between the two time limits is justified by the fact that the decision task of the responders requires more time to be completed (due to the strategy method adopted). Participants in the low time-pressure condition (tp0) had 180 s for both kinds of decisions. A post-questionnaire confirmed that the manipulation was successful.5 In addition, we introduced monetary rewards to incentivise participants to exert effort in the memory task. Most research examining cognitive load did not employ real incentives (for an exception, see Benjamin, Brown, & Shapiro, 2006). In order to test whether there is an interaction effect between monetary incentives and cognitive load, we set two levels of incentives: € 0.30 per digit in the high-incentive condition (i1) and € 0.03 per digit in the low-incentive condition (i0). The payment rule for the memory task is detailed in the next subsection. 2.2. Interaction structure Four distinct stages can be identified in the experiment. In Stage 1, each participant is asked to mentally solve five multiplication problems.6 The problems are presented successively7 and involve two 2-digit numbers such that they result in a 3digit number (e.g., 14  16 = 224). Each participant is asked to memorize the results of the problems and to keep them in mind until Stage 3, where she will be asked to recall them. If a participant calculates more than two problems correctly, she is given a provisional endowment of € 15; otherwise, she is given a provisional endowment of € 7. These endowments constitute the amount of money to be divided in the UG. To prevent participants from making their decisions in advance, they are informed about the size of these endowments only when decisions are made in the UG. To incentivise more choices, the actual performance in the multiplication task, and thus the actual endowment to be divided in the UG, is revealed only at the end of the experiment. In Stage 2 an UG is played. The strategy vector method is employed to collect choices in the game:8 participants are asked to make decisions for each of the two roles in the game and for each of the two possible levels of endowment. As proposer (referred to as role A), a participant has to state the offer she intends to make by choosing any amount between € 0 and the endowment (in steps of € 1). As responder (referred to as role B), she has to state her reaction (i.e., acceptance or rejection) for any possible offer. To summarize, subjects have to enter four distinct action profiles in the following order: proposer in the high endowment condition, proposer in the low endowment condition, responder in the high endowment condition, and responder in the low endowment condition.9 In Stage 3, each participant is first asked for an assessment of her own and her partner’s performance in the computations and in the recall task. Thus, four estimates are collected. Each correct guess is rewarded with € 0.50. The participant is then asked to recall the results of the multiplication problems in the same order of appearance as in Stage 1. Real incentives are provided for the recall task; specifically, when the recalled number is equal to the computed number, each digit equal to the digit in the correct solution is rewarded with a certain amount of money (either € 0.30 or € 0.03).10 In Stage 4, each participant is asked about her beliefs of acceptance of the offer made, i.e., to estimate how likely the offer she made is accepted by the responder. This question is asked for both endowment levels. The task is incentivised and the payoffs for each combination of estimated probability and action of the responder are detailed in Table A.2.11

5 Participants indicated on a 5-point Likert scale (ranging from ‘‘not at all’’ to ‘‘very much’’) whether they felt under time pressure while making decisions in the UG. The average scores (3.34 and 1.51 for participants in the high time-pressure and in the low time-pressure condition respectively) were significantly different (Wilcoxon rank-sum test, p-value < 0.001). 6 The purpose of the multiplication task is to establish endowment legitimacy (Cherry, Frykblom, & Shogren, 2002). One might argue that this analytic task favours the activation of analytical deliberative processing, affecting this way subsequent decision-making. If this is indeed the case, it would mitigate the effect of our manipulation, not enhance it. 7 Once the participants enter the result, they pass to the next problem and cannot return to previous screens. 8 One might argue that having the participant serve in both the roles of proposer and responder affects some aspects of the decision-making process. Comparing ultimatum decisions elicited alternatively through the strategy vector method and the sequential play method, Oxoby and McLeish (2004) found no behavioural differences (neither in the mean and the distribution of offers nor in mean acceptance rates). However, even in case method effects were present, they would remain constant across treatments, since the same elicitation method is maintained across treatments. 9 Participants failing to submit one or more choices pay a flat penalty of € 1 to be subtracted from the show-up fee. 10 For example, if the correct solution of a problem is 350, and the computed number is 358, but the number recalled is 350, then the participant earns nothing for this recall. If the number recalled is 358 (i.e., equal to the computed number), the participant is paid for 2 out of 3 digits. This payment procedure ensures against the adoption of ‘‘ad hoc’’ values to simplify recall. 11 The payoffs in Table A.2 are defined according to a quadratic scoring rule (for a detailed explanation of the rule, see Schotter & Sopher, 2007). The probabilities of acceptance are defined over the values {0, 20, 40, 60, 80, 100}. According to the rule the payoffs associated to   certain beliefs (pb) are defined as 1 1 follows: when the responder accepts, pAb ¼ 2  10;000  ð2  ð100  pa Þ2 Þ ; similarly, when the responder rejects, pRb ¼ 2  10;000  ð2  ð100  pr Þ2 Þ . The rule penalizes both the situation in which less than full probability was assigned to an event when it happens and the situation in which some probability was assigned to an event when it does not happen.

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D. Cappelletti et al. / Journal of Economic Psychology 32 (2011) 940–950 Table A.1 Treatments. Time pressure Low

High

Incentive low Cognitive load

Low High

cl0.tp0.i0 cl1.tp0.i0

cl0.tp1.i0 cl1.tp1.i0

Cognitive load

Low High

cl0.tp0.i1 cl1.tp0.i1

cl0.tp1.i1 cl1.tp1.i1

Incentive high

Table A.2 Quadratic scoring rule for the acceptance beliefs. Certainty of acceptance

0%

20%

40%

60%

80%

100%

Earning when accepted Earning when rejected

0.00 2.00

0.70 1.90

1.30 1.70

1.70 1.30

1.90 0.70

2.00 0.00

Table A.3 Proposer offers: summary statistics. Treatment

Pooled cl1.tp0.i0 cl1.tp0.i1 cl1.tp1.i0 cl1.tp1.i1 cl0.tp0.i0 cl0.tp0.i1 cl0.tp1.i0 cl0.tp1.i1 a b

High endowment (€ 15)

Low endowment (€ 7)

N

Mean

Std. dev.

Median

N

Mean

Std. dev.

Median

346a 48 46 40 36 48 48 43 37

6.19 5.73 6.22 5.80 6.42 6.00 6.23 6.63 6.68

1.70 1.57 2.24 2.21 1.61 1.41 1.13 1.42 1.62

7.00 6.00 7.00 7.00 7.00 6.00 6.00 7.00 7.00

374b 48 46 47 46 48 48 45 46

2.96 2.69 3.02 2.68 3.07 2.88 3.15 2.98 3.22

0.92 0.80 1.24 0.84 0.93 0.70 0.92 0.94 0.79

3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00

30 missing observations are due to participants failing to submit their proposal. 2 missing observations are due to participants failing to submit their proposal.

After having stated their acceptance beliefs, the participants are informed about their actual role in the game – proposer or responder – and about the relevant endowment for the UG – high or low. The payoffs for each of the stages and the total payoff are then communicated to each participant.12 The sequence of stages just described refers to the conditions with cognitive load (i.e., cl1). The conditions without cognitive load (i.e., cl0) differ only in the order of Stage 2 and Stage 3, so that the memory task and the UG are not concurrent. 2.3. Participants and procedures Three hundred and seventy-six students (154 males and 222 females) at the Friedrich Schiller University in Jena (Germany) participated in the experiment. They were randomly assigned to one of the eight conditions described above. Participants were recruited through the online recruitment system ORSEE (Greiner, 2004). On their arrival at the laboratory, participants were seated in computer-equipped cubicles that do not allow communication or visual interaction among the participants. In order to prevent the use of external aids (e.g., paper and pencil, cellphone) during the experimental tasks, participants were asked to leave their personal belongings at the entrance. The experiment was programmed and conducted using the z-Tree software (Fischbacher, 2007). Participants received written instructions,13 which were first read individually by the participants and then aloud by a German-speaking collaborator to establish common knowledge. Understanding of the instructions was tested through an on-screen questionnaire that subjects were asked to answer before the experiment. Including payment, sessions lasted for about 50 min, and participants earned, on average, € 9.57 (including a show-up fee of € 2.50).

12 If one or both participants in a pair fail to submit the strategy profile relative to their actual role and the relevant endowment, both receive nothing for the UG task, since payoffs cannot be calculated. The earnings from Stage 4 are paid only to the proposers. 13 The instructions are available upon request from the authors.

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3. Results and discussion 3.1. Offers Table A.3 provides descriptive statistics for offers in the UG, in the high-endowment (€ 15) and low-endowment (€ 7) conditions. The behaviour of proposers in this experiment is in line with that generally observed in UG experiments. In the highendowment condition, the mean offer is € 6.19, which represents 41.27% of the pie, and the median offer, which represents 46.67% of the pie, corresponds to one of the two nearly equal splits available to the proposer. In the low-endowment condition, both the mean and the median offers are very close to the nearly equal split of offering € 3 to the counterpart. These results reveal, thus, a strong concern of proposers for fairness. The comparison of behaviour across treatments shows that, when bargaining over the high-endowment, proposers tend to offer more under higher time pressure (keeping constant other experimental factors). This patterns is corroborated by non-parametric tests (Wilcoxon Rank-sum Test, WRT). Specifically, in the absence of cognitive load and with incentives kept constant across comparisons, a statistically significant difference in the distribution of offers is registered when comparing cl0.tp0.i0 vs. cl0.tp1.i0 (WRT, p-value = 0.025) and cl0.tp0.i1 vs. cl0.tp1.i1 (WRT, p-value = 0.031). The other pairwise comparisons between treatments differing in the level of only one factor do not identify any significant main effect of the other experimental factors (WRT, all p-values > 0.1). Thus, only time pressure has a statistically significant impact on choices in the high-endowment condition. This allows us to pool together the data that share the same level of time pressure but differ in the level of other factors. The analysis conducted on the pooled data confirms that proposers tend to send more under higher time pressure. Fig. B.1 shows the distribution of choices in the two alternative time pressure conditions. The median offer is equal to 7 in the high-time pressure condition (tp.1) and equal to 6 in the low-time pressure condition (tp.0). The difference between the two distributions of offers is statistically significant (WRT, p-value = 0.005). As Fig. B.1 illustrates, the fair offer 7 is chosen more frequently under high time pressure than under low time pressure (44.2% vs. 35.3%, respectively). However, a Pearson’s Chi-square test shows that the two frequencies are not statistically different (pvalues = 0.112). Compared to the high-endowment condition, less variability in offers across treatments is observed in the low-endowment condition. Moreover, when replicating the analysis performed for the high-endowment condition, no main effects of the experimental factors on offers in the low-endowment condition are detected (WRT, all pvalues > 0.1). Table A.4 reports the results of a Tobit Regression of offers in the UG. This specification has been chosen to account for the limits imposed to the offers in the experiment. The dependent variable Offer is regressed against the explanatory treatment variables – Time Pressure, Cognitive Load, and Incentives – and on the number of correct recalls (Correct Recall) in the memory task.14 This last variable provides a proxy of the actual effort in the memory task and a control on possible wealth effects in the game. The interactions between Cognitive Load and Time Pressure (TP  CL), Cognitive Load and Incentives (Inc  CL), and Cognitive Load and Correct Recall (CR  CL) are also included in the model. The results of the regression analysis confirm that time pressure has a significant positive impact on offers made in the high-endowment condition, while the other explanatory variables do not have any significant effect. In the low endowment condition, only incentives and correct recalls have a marginally positive, respectively negative significant impact (10% level of significance) on the amount offered. In both endowment conditions, the model as a whole is statistically significant, although the explanatory power of the two estimations is quite low (i.e., Pseudo R2 6 0.02). Next, we summarize and discuss the results obtained from the comparison of offers across treatments. Result 1. Time pressure leads proposers to increase their offers. Our first and most important result is that, when deliberation is constrained by the presence of a time limit for making decisions, more reliance on instinctive affective processing induces proposers to raise their offers. In Section 1.2 we argued that, when they are under time pressure, proposers may rely more on the most salient sharing heuristic, i.e., splitting evenly, than when they are not. The data show that this is not the case. Although it is true that the allocation 60%:40%, which is the most equitable split available to proposers, is chosen more frequently under high time pressure than under low time pressure, the difference is not statistically significant. Thus, the increase in offers observed under time pressure is not entirely explained by increased attraction to the focal equitable split. The positive effect of time pressure on the amount offered is significant only in the high-endowment condition. This can be attributed to the low variance observed in the low-endowment condition, which may be caused by the limited number of options available to proposers in this condition. In addition, participants may have perceived low-endowment choices as less relevant. The actual level of endowment (high or low) in each pair was determined by the performance in the computation task of the participant in the actual role of proposer. Specifically, the high endowment was given to those proposers who solved three or more computation problems correctly. The mean estimation of the number of problems correctly solved

14 Here we do not employ the number of rewarded recalls, but the number of correct recalls regardless of the correctness of the computation because it provides a better measure of actual cognitive effort in the memory task.

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Freq (%)

0

10

20

30

40

High time pressure Low time pressure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Offer Fig. B.1. Proposer Offers (pooled): Distribution of choices.

Table A.4 Proposer behaviour (Tobit Regression). Offer

Coeff. (Std. err.) High endowment

Low endowment

Time pressure Cognitive load Incentives Correct recall TP  CL Inc  CL CR  CL Cons.

0.507 (0.257)⁄⁄ 0.009 (0.594) 0.126 (0.255) 0.038 (0.036) 0.337 (0.366) 0.510 (0.365) 0.042 (0.051) 6.436 (0.438)⁄⁄⁄

0.057 (0.140) 0.318 (0.326) 0.242 (0.140)⁄ 0.033 (0.020)⁄ 0.029 (0.198) 0.155 (0.198) 0.005 (0.027) 3.210 (0.241)⁄⁄⁄

Obs Prob > F Pseudo R2

346 0.009 0.014

374 0.005 0.020

⁄

10% significance level. 5% significance level. ⁄⁄⁄ 1% significance level. ⁄⁄

was 3.26 for participants themselves and 3.24 for their partners. These performance estimations suggest that, on average, participants expected to bargain over the high endowment. Result 2. Proposers who are under cognitive load do not behave differently from proposers who are not. Contrary to what observed in other studies, cognitive load did not have any effect on choices in this experiment. The cognitive load manipulation we used – requiring participants to remember a string of numbers while performing the task of interest – is common in psychology studies (e.g., Benjamin et al., 2006; Hinson et al., 2003; Roch et al., 2000; Shiv & Fedorikhin, 1999). Unlike previous studies, we incentivised the task with a monetary reward for each digit correctly recalled. This difference in the procedure may account for the fact that, unlike previous studies, we did not find any effect of cognitive load. In a series of Dictator Game experiments, Hauge, Brekke, Johansson, Johansson-Stenman, and Svedsäter (2009) applied a cognitive load manipulation using non negligible incentives for the memory task and, like us, did not find any significant effect of the manipulation. We introduced different levels of incentives for the memory task to check for possible interaction effects between cognitive load and incentives. One might argue that providing small incentives can lead individuals to be disengaged from a task. Gneezy and Rustichini (2000), in fact, found that performance in a test was lower when low incentives were offered than when no compensation was offered. From this point of view, when incentives are low the cognitive load manipulation might not affect offers because low incentives lead to a motivation crowding-out, so that subjects do not invest any energy into the

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memory task. The results of this experiment show that there is no significant interaction effect between incentives and cognitive load on ultimatum offers. Result 3. Cognitive load does not affect ultimatum offers independent of the level of monetary incentives for the memory task. The analysis of recall performance allows us to further rule out the motivation crowding-out: recall performances when incentives are low do not significantly differ from recall performances when incentives are high (WRT, pvalue = 0.942).15 A positive, although marginal, main effect of incentives on offers is found when proposers split the low endowment. When the incentives are high, participants have the opportunity to earn a non-negligible amount of money in the memory task, and the opportunity to earn this additional amount seems to lead proposers to make higher offers in the UG. Offers in the low endowment condition are also negatively, although marginally, influenced by the number of correct recalls in the memory task, which can be considered as a measure of actual cognitive effort exerted by participants in the memory task. This finding suggests that when the amount of money to be divided is low (€ 7), their cognitive investment motivates proposers to demand more for themselves, possibly to compensate their effort. Participants’ estimations of their performance in the memory task are significantly higher than those of their partners’ performance. Thus, it could also be that proposers try to retain more for themselves because they feel they deserve it (e.g., Konow, 2000). Alternatively, the number of correct recalls could indicate cognitive abilities (Frederick, 2005). According to this interpretation, cognitively more able proposers seem to behave more selfishly, although previous findings on the relationship between cognitive abilities and offers are mixed. Benjamin et al. (2006) found a weak negative relationship between cognitive abilities and giving in a Dictator Game and Ben-Ner, Kong, and Putterman (2004) found the same relationship only for women, whereas Brandstätter and Güth (2002) did not find any relationship, either in the Dictator or in the Ultimatum Game. 3.2. Offers and minimum acceptance thresholds We hypothesized that in reaching their decision about the amount to offer, proposers under cognitive constraints would engage more in heuristic reasoning that leads them to choose the salient equitable split. We have previously seen that proposers are not significantly more likely to rely on the equality heuristic when they are under time pressure than when they are not, suggesting that strategic thinking may still be at work. Comparing the offer made and the minimum acceptance threshold (hereafter MAT) set when playing the role of responder allows us to gain some insights into the relative weight of the strategic and the other-regarding components in increasing offers under time pressure. Indeed, subject to false consensus (Kuhlman & Wimberley, 1976), the proposer may expect the MAT of the responder to equal her own MAT when playing the role of responder. Playing strategically, the proposer thus should offer at least her own MAT. The amount that exceeds the minimum acceptable offer can be attributed to other-regarding concerns. The mean MAT16 is € 3.45 in the high-endowment condition and € 2.20 in the low-endowment condition. The comparison of MATs across treatments shows that in both endowment conditions only time pressure has a statistically significant impact on MAT, with MAT being higher under high time pressure. As we did for offers, we pooled together data that do not differ in terms of time pressure. In the high endowment condition, the median MAT is 4 under high time pressure and 3 under low time pressure, and the difference between the two distributions is statistically significant (WRT, p-value = 0.033). In the low endowment condition, the median MATs are 3 and 2 under high and low time pressure, respectively, and the difference between the two distributions is statistically significant (WRT, p-value = 0.002). Next, we look at the difference between offers and MATs. In the high-endowment condition, offers and MATs are positively correlated (Spearman’s Rank Correlation q = 0.352, p-value < 0.001). In particular, 14.4% of these participants set their MATs equal to their offer in the UG. The mean spread between the offer and the MAT is € 2.64, and the spread between the two distributions is statistically different from 0 (WRT, p-value < 0.001). In the low-endowment condition, the positive correlation between offers and MATs is lower than that in the high-endowment condition (Spearman’s Rank Correlation q = 0.237, p-value < 0.001). However, the percentage of participants equating their offers with their MATs is higher (39.9%); consequently, the spread between the MAT and the offer is lower than that in the high-endowment condition (mean € 0.73). Again, this spread is different from 0 (WRT, p-value < 0.001). Therefore, when setting their offers, most proposers follow a ‘‘mark-up strategy’’ in which they send to the responders more than the minimum amount that they would accept themselves as responders. Interestingly, when regressing the spread between MATs and offers against the explanatory factors employed in the previous model estimations (see Table A.4), no significant effect is registered in either of the endowment conditions. Moreover, the joint hypothesis of null effects is not rejected at the conventional 5% level of significance. The results of the comparison of offers and MATs can be summarized as follows.

15 Different levels of incentives do not influence recall performance even when controlling for cognitive load (WRT, p-value = 0.186 for the comparison in the cognitive load condition; p-value = 0.160 for the comparison in the no cognitive load condition). 16 MAT can be computed only for participants with a monotonic acceptance pattern. Only a small portion of participants (3,13% in the high-endowment and 3,48% in the low-endowment condition) provided non-monotonic response vectors.

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Result 4. Offers exceed the minimum acceptable offers that participants state when playing the role of responder. This positive mark-up is constant across treatments. Proposers offer at least the minimum amount they believe responders will accept (proxied by their own MAT). On average MATs, as well as offers, are higher under high time pressure than under low time pressure, suggesting that strategic considerations are important. We said that offering more than the expected minimum acceptable offer can be ascribed to other-regarding concerns. On average, the difference between the amount proposers offer and the minimum amount they believe responders will accept (proxied by their own MAT) is positive, indicating the presence of other-regarding concerns. In Section 1.2 we considered two competing hypotheses about the impact of other-regarding concerns when cognitive resources are constrained. Specifically, impairing deliberative processing would increase other-regarding concerns according to the intuitionist view, while it would reduce them according to the rationalist view. Our results show that the difference between the amount offered and the expected minimum acceptable offer remains constant across treatments. Thus, the increase in offers observed under time pressure seems not to be due to variation in other-regarding concerns, supporting the role of fear of rejection. 3.3. Beliefs To conclude our analysis, we briefly look at proposers’ beliefs of acceptance of the offer made. In the high-endowment condition, the median estimated probability of acceptance is equal to 80% in all treatments and average values are in the range 74.5–83.3%. A series of non-parametric tests (WRT) does not detect any significant influence of the experimental factors on the reported confidence values. In the low-endowment condition, confidence of acceptance is characterized by higher volatility across treatments. Median values are either equal to 60% or 80% and average values are in the range 64.6–80.4%. An Ordinary Least Squares analysis in which beliefs are regressed against the explanatory variables employed in the model estimation reported in Table A.4 shows the lack of a systematic impact of the experimental factors on beliefs in both endowment conditions. The joint null hypothesis that all the explanatory factors have no impact on beliefs is not rejected at the conventional 5% level of significance. Consequently, the full estimation results are not reported. Result 5. Proposers’ beliefs of acceptance of the offer made remain constant across treatments. This result is particularly interesting when considering the increase in offers observed under time pressure: although offers increase in the high-time pressure condition, they are not perceived as more likely to be accepted. 4. Conclusions and further research This study examined the influence of affect on proposer offers in the Ultimatum Game using a dual-system approach. To enhance the influence of spontaneous affective reactions on behaviour, we inhibited deliberative processes by imposing time pressure and cognitive load on proposers. Our main finding shows that greater reliance on instinctive affective processes due to time pressure leads proposers to increase their offers. This increase is not explained by more reliance on an equality heuristic, suggesting thus the presence of strategic thinking. Future research should further investigate the driving forces behind the increase in offers observed under time pressure, i.e., whether it is determined predominantly by strategic considerations or by other-regarding concerns. To get some insights into this, we compared offers and minimum acceptable offers stated by proposers who were asked what they would accept as a responder. This comparison leads us to surmise that higher offers under time pressure are not due to variation in other-regarding concerns, and thus to favour the strategic explanation for the observed increase in offers. However, these considerations are based on potential false consensus effects, i.e., the tendency of people to think that others behave as they do. Further research is needed to shed more light on the relative contribution of the strategic and the otherregarding components in increasing offers under time pressure. Further research is also needed to understand the lack of effect of the cognitive load manipulation that we reported in this experiment. Different from the cognitive load procedure commonly used in psychology, we introduced financial incentives for the memory task. Future research should investigate whether this methodological difference may account for the lack of effects of the cognitive load manipulation as reported here. The inconsistency of our results with previous findings suggests that slightly different cognitive load manipulations may have different effects on decision-making process. Acknowledgements The authors gratefully acknowledge the helpful advice of anonymous referees and of the associate editor Simon Gächter. The authors thank James Konow for thoroughly reading the paper and providing constructive feedback. Participants in seminars and conferences are acknowledged for their comments and suggestions. The usual caveats apply.

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