Economic principles in communication: An experimental study

Journal of Theoretical Biology 363 (2014) 62–73

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Economic principles in communication: An experimental study Kris De Jaegher a,n, Stephanie Rosenkranz a, Utz Weitzel b a b

Utrecht University School of Economics, Utrecht University, Utrecht, The Netherlands Institute of Management Research, Department of Economics, Radboud University Nijmegen, Nijmegen, The Netherlands

H I G H L I G H T S








We investigate how economic principles affect communication, focusing on Horn’s rule. Focal point theory, the intuitive criterion, and evolutionary game theory are compared. Signaling games are considered where these theories generate discriminatory hypotheses. We let participants play the signaling games in an economic laboratory experiment. We find evidence both for focal point theory and for evolutionary game theory.

art ic l e i nf o

a b s t r a c t

Article history: Received 22 April 2014 Received in revised form 9 July 2014 Accepted 31 July 2014 Available online 13 August 2014

This paper experimentally investigates how economic principles affect communication. In a simple sender–receiver game with common interests over payoffs, the sender can send a signal without a pregiven meaning in an infrequent or frequent state of the world. When the signal is costly, several theories (focal point theory, the intuitive criterion, evolutionary game theory) predict an efficient separating equilibrium, where the signal is sent in the infrequent state of the world (also referred to as Horn's rule). To analyze whether Horn's rule applies, and if so, which theory best explains it, we develop and test variants of the sender–receiver game where the theories generate discriminatory hypotheses. In costly signaling variants, our participants follow Horn's rule most of the time, in a manner that is best explained by focal point theory. In costless signaling variants, evolutionary game theory best explains our results. Here participants coordinate significantly more (less) often on a separating equilibrium where the signal is sent in the frequent state if they are primed to associate the absence of a signal with the infrequent (frequent) state of the world. We also find indications that a similar priming effect applies to costly signals. Thus, while the frequency with which participants follow Horn's rule in costly signaling variants is best explained by Horn's rule, the priming effect shows that some of our participants' behavior is best explained by evolutionary game theory even when signals are costly. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Horn's rule Signaling theory Pragmatics Economic laboratory experiment

1. Introduction De Saussure (1916) argued that the meaning of signals in communication is purely conventional. For instance, a convention may evolve between drivers such that a driver flashes her headlights to an oncoming driver if there is a speed camera ahead, and does not flash her headlights otherwise. But if communication is indeed purely conventional an alternative convention would then be equally likely to evolve, where drivers flash their headlights when there is no speed camera ahead, and do not flash them otherwise. Yet, such a convention strikes us as absurd, as drivers

n

Corresponding author. Tel.: þ 31 30 253 9964. E-mail address: [email protected] (K. De Jaegher).

http://dx.doi.org/10.1016/j.jtbi.2014.07.035 0022-5193/& 2014 Elsevier Ltd. All rights reserved.

would then constantly incur the cost of flashing their headlights, given that most of the time there is no speed camera ahead. An economic principle seems to be at work, eliminating such an absurd signaling convention.1 The linguistic field of pragmatics starts from the premise that economic principles play a role in language use. Following a classical example by Grice (1975), p. 55, consider the statement

1 The fact that economic principles may determine what type of communication is used was stressed by Zipf (1949) and Martinet (1955). Applications include the use of a compositional language/grammar to limit the number of signals (Selten and Warglien, 2007), the use of contrasting signals or of compositionality to reduce noise in communication (Jäger, 2008a; Nowak and Krakauer, 1999), and the relegating of costlier, more precise language to more important states of the world, as witnessed by the use of jargon (Crémer et al., 2007).

K. De Jaegher et al. / Journal of Theoretical Biology 363 (2014) 62–73

“Miss X produced a series of sounds that corresponded closely with the score of ‘Home Sweet Home’. Literally speaking, the producer of such a statement is not claiming anything else than that Miss X sang ‘Home Sweet Home’, yet listeners will often interpret that Miss X is a terrible singer, seemingly inferring from the speaker's verbosity that something unusual is going on. Grice refers to this as pragmatic inference, and Horn (1984) argues that this underlies the general principle of language use that (un) marked states of the world receive (un)marked expressions. We here refer to this principle as Horn's rule. Given the clear link of pragmatic inference with game theory, the last decade has seen the emergence of the field of gametheoretic pragmatics (for overviews, see Benz et al. (2005), Jäger (2008a) and De Jaegher and van Rooij (2014)). A key sender– receiver game analyzed in this theoretical literature (see e.g. Parikh (1991, 2000, 2001), van Rooij (2004)), which we reduce here to its most basic form and refer to as the Standard Costly signaling game, takes the following form. The sender (she), but not the receiver (he), knows whether a frequent state of the world F (probability pF) or an infrequent state of the world I (probability ð1  pF Þ) occurs, where pF 40.5. The sender has a single signal available, which in each state of the world she can either send or not send.2 The receiver observes whether or not the signal was sent, and then guesses the state. The sender and the receiver both receive an identical payoff UðrjsÞ, where r ¼ I; F is the guess that the receiver makes and s ¼ I; F is the state. When having sent the signal, the sender additionally incurs a cost c, not incurred by the receiver. It is assumed that UðsjsÞ 4 UðrjsÞ (with r a s), so that both sender and receiver prefer that the receiver guesses the correct state, and that , UðsjsÞ  UðrjsÞ 4c so that in each state the sender prefers to send the costly signal rather than not to send it, if this leads the receiver to make the correct instead of the wrong guess.3 Finally, it is assumed that pF UðFjFÞ þ ð1  pF ÞUðFjIÞ 4pF UðIjFÞ þ ð1  pF ÞUðIjIÞ, meaning in terms of the driver example that a driver without information finds it preferable to speed. The Standard Costly signaling game has three perfect Bayesian equilibria (Fudenberg and Tirole, 1991). First, a pooling equilibrium where the sender never sends a signal and where the receiver always guesses the more frequent state of the world.4 Further, two separating equilibria: an efficient separating equilibrium obeying Horn's rule where the sender only sends the signal in state I (henceforth, separating-I equilibrium), and an inefficient separating equilibrium where the sender only sends the signal in state F (henceforth, separating-F equilibrium). In this paper, we design a laboratory experiment to test both whether Horn's rule applies, and if so, which of several alternative theories provides the best rationale for Horn's rule. The problem with answering the second question is that mere observance of Horn's rule in the Standard

2 In binary signaling games, the sender is often modeled as always sending one of two available signals (e.g. Hofbauer and Huttegger (2008)). With two states of the world, the fact that an available signal was not sent can be interpreted as a message as well. The model where the sender either sends or does not send a single signal is therefore analytically identical to a model where the sender always sends one of two signals.. 3 In economics signaling literature, this type of game is referred to as a cheap talk signaling game with nominal signaling costs (Blume et al., 1993). This contrasts both with Crawford and Sobel's (1982) model of cheap talk, where signals are costless, and with Spence's (1973) model of costly signaling, where signals are differentially costly, and may be prohibitively costly to send in some states. In this paper, we only treat cheap talk signaling games with either nominal signaling costs or zero costs, which for ease of reference we here refer to respectively as costly signaling games (not to be confused with Spencian costly signaling) and as cheap talk signaling games. For a critical appraisal of the signaling literature from the perspective of pragmatics, see Sally (2005). 4 More correctly, there is a range of perfect Bayesian pooling equilibria, where the receiver may plan to do I when receiving a signal with different frequencies, which should not be too high.

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Costly signaling game does not allow us to identify the best rationale for this rule. For this reason, we implement variants of the Standard Costly signaling game (see Table 1) for which alternative theories do predict a different equilibrium. In the Modified Costly signaling game, the payoffs of the signaling game are modified such that pF UðFjFÞ þð1 pF ÞUðFjIÞ 4 pF UðIjFÞ þ ð1  pF ÞUðIjIÞ In terms of the driver example, even though speed cameras continue to be rare, traffic fines are now so high that, in absence of any information, drivers do not speed. The Standard Cheap talk signaling game and the Modified Cheap talk signaling game are identical to the two costly signaling games, except that the signal is now costless. Our experiment compares to the growing number of papers studying the evolution of communication in the laboratory in the following ways. The difference with experiments in the field of experimental pragmatics (for an overview, see Noveck and Reboul (2008)) is that these experiments look at the pragmatic use of natural language in the laboratory, whereas we look at the pragmatic use of an (extremely simple) artificial language. This makes our experiment similar to experiments in what may be referred to as experimental semiotics (see Galantucci (2009), for an overview): following a subpart of this literature, our participants can make use of pre-given signals without a pre-given meaning, and cannot create their own signals. Finally, specific about our paper is that it is an economic experiment: this is important, as in our experiment participants incur a monetary cost of sending the single available signal, making the economic principle relevant. To our knowledge, our paper is the first economic laboratory experiment on Horn's rule. In existing economic communication experiments, signals typically have a commonly known meaning, and the subject is either pre-play communication in commoninterest coordination games (for an overview, see Crawford (1998)), or signaling in conflict-of-interest games, where signals are either cheap talk following the model of Crawford and Sobel (1982) (e.g. Cai and Wang (2006), Sánchez-Pagés and Vorsatz (2007)), or costly in the sense of Spence (1973) and Zahavi (1975) (e.g. de Haan et al., 2011). Exceptions are Blume et al. (1998) and Selten and Warglien (2007), where signals do not have a pre-given common meaning, and where the focus lies on the learning of an artificial language in the laboratory. Yet, in these papers, costly signals are not considered. A recent paper where signals both have nominal costs and no pre-given meaning, is Dos Santos et al. (2012). Their focus is on the evolution of an artificial language, comparing local competition (highest performing participant in a local group receives a reward) to global competition (highest performing participant in global group receives reward), and looking at the impact of whether or not the signal is costly. In our paper, participants' interests coincide, with the exception that the receiver does not incur a cost when the sender sends a costly signal. In Sections 1.1, 1.2, and 1.3, we compare the predictions of three different theories for the four games we consider, as summarized in Table 1. While all three theories make the same predictions for the Standard Costly signaling game, the predictions differ for the other games in Table 1, justifying the choice of these games. 1.1. Focal point theory In case a game has multiple equilibria, focal point theory (Schelling, 1960) posits that if one of the equilibria is salient because it possesses some unique feature not possessed by other equilibria (a focal point), this will create mutual expectations among the players of the game that this equilibrium will be played. Parikh (1991, 2000, 2001) applies focal point theory to the Standard Costly signaling game, and predicts that the fact that

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K. De Jaegher et al. / Journal of Theoretical Biology 363 (2014) 62–73

Table 1 Four signaling games. pF 1  pF

UðIjIÞ  UðFjIÞ 4 UðFjFÞ  UðIjFÞ

pF 1  pF

UðIjIÞ  UðFjIÞ 4 UðFjFÞ  UðIjFÞ

c 40 Standard costly signaling game Modified costly signaling game c ¼ 0 Standard Cheap talk signaling game Modified cheap talk signaling game

a single equilibrium is efficient makes this equilibrium salient, and will cause it to be played. The prediction extends to the Modified Costly signaling game. For cheap-talk signaling games, Lewis (1969) applies focal point theory when pointing out that signals may have intrinsic features, making their meaning salient. Yet, the single signal which the sender can send in our experiment does not have such features.5 As summarized in Table 2 in Section 2.2, Column 1, focal point theory therefore predicts the separating-I equilibrium for both costly signaling games, and makes no predictions on which equilibrium is selected for the cheap talk signaling games.

1.2. Pooling-based intuitive criterion The intuitive criterion (Cho and Kreps, 1987) is one of several equilibrium refinements that capture the same intuition, loosely referred to as forward induction arguments (for overviews, see Fudenberg and Tirole (1993) (Chapter 11), and Hillas and Kohlberg (2002)). We focus on the intuitive criterion, because it most closely relates to what Grice (1975) calls pragmatic inference. Applied to our model, consider a perfect Bayesian equilibrium En where sending the signal is out-of-equilibrium, and where the receiver makes guess rn. Let it be equilibrium dominated for the sender in state s to send the signal, meaning that Uðr njsÞ 4 max UðrjsÞ  c. In r words, let the best guess that the sender in state s can get after n sending the signal, be worse than the guess r that she gets in equilibrium En by not sending the signal. Knowing this, a receiver who expects that equilibrium En will be played and still receives the signal should believe that it was sent in state s´, with s0 as, and should guess s0 . Let it now further be the case for the sender in state s´ that Uðs0 js0 Þ  c 4 U nðr njs0 Þ. In words, let the sender in state s´, anticipating on the receiver's response to the signal, prefer to send the signal and obtain response s´, rather than to follow the equilibrium (by not sending the signal) and obtain response rn.6 Then equilibrium En fails Cho and Kreps' (1987) intuitive criterion.7 It is easily checked that in both costly signaling games, the pooling equilibrium fails the intuitive criterion, but both separating equilibria meet the intuitive criterion as the signal is then not out-of-equilibrium. van Rooij (2008), however, formulates a variant of the intuitive criterion, referred to as the pooling-based intuitive criterion, which always takes as a starting point the pooling equilibrium where the signal is never sent. The rationale is that if we want to know how individuals come to use a signaling system, we should explain how they come to do this if they are 5 In a signaling experiment by Blume et al. (2001), in order to signal three states of the world the sender can either send signals labeled by the letters A, B, C or D. Participant senders predominantly send only the first three letters only, and send letter A in state 1, letter B in state 2, etc., suggesting that participants coordinate on a focal point. In our experiment, the sender can only choose between sending a single, unlabeled signal, or not sending this signal, so that focal points of the form observed by Blume et al. are not relevant. 6 For a more general signaling model with more than two states of the world, the second condition says that if the receiver believes that the signal cannot have been sent in state s, the sender in state s´ prefers sending the signal even if the receiver with such beliefs makes the guess that is the worst possible to her. 7 For cheap talk games, a somewhat related equilibrium refinement is neologism proofness (Farrell, 1993), but this is based on signals having a pre-given, commonly known meaning, which we do not assume here.

initially not using a signaling system.8 If, in the pooling equilibrium, sending the signal is equilibrium dominated for the sender in state s, then the pooling-based intuitive criterion eliminates the separating equilibrium where the costly signal is sent in state s, so that the separating-F equilibrium is eliminated in the Standard Costly signaling game, and the separating-I equilibrium is eliminated in the Modified Costly signaling game. Yet, for the two cheap signaling games, the pooling-based intuitive criterion does not provide any predictions, because in the pooling equilibrium there is no state where it is equilibrium dominated for a sender to send the costless signal (see Table 2 in Section 2.2, Column 2). 1.3. Pooling-based evolutionary approach The theories in the previous two subsections are based on the assumption that players are rational. A separate stream of signaling and game-theoretic pragmatics literature uses evolutionary game theory to model which equilibria less sophisticated players may learn to play in signaling games (for an overview, see Huttegger and Zollman (2011)). In such models, players are repeatedly and randomly paired to play a signaling game. Typically, pairs are drawn from a single population, where randomly one player is assigned the role of sender and the other player is assigned the role of receiver; alternatively, senders and receivers constitute separate populations (Hofbauer and Huttegger, 2008; De Jaegher, 2008).9 More successful strategies gradually become more frequent in the population(s), following a dynamic process, typically the replicator dynamics. In terms of learning, a first interpretation is that the individual player imitates the strategies of successful other players (Schlag, 1998). A second interpretation is that the individual player has a “population of ideas” in his mind, in the form of several strategies he considers playing (Börgers and Sarin, 1997).10 This population of ideas is subject to differential replication, in that the player's propensity to play any specific strategy is proportional to the success of this strategy in the past, and is subject to mutation, in that players may make small mistakes. Given this second interpretation, evolutionary game theory is relevant even if a single sender and receiver repeatedly interact. Because focal point theory and the poolingbased intuitive criterion are only relevant to the coordination in an individual sender–receiver pair, to keep the predictions of these two theories comparable to the predictions of evolutionary game theory, we adopt the second interpretation, and interpret the populations of senders and receivers from the literature as the populations of ideas of an individual sender and receiver. The question mainly addressed in this literature is whether players of signaling games can unlearn to play uninformative equilibria. As shown by Wärneryd (1993), pooling equilibria like the ones in the Standard and Modified Cheap talk signaling games are never evolutionarily stable. Intuitively, in a pooling equilibrium the receivers are already doing part of what they are supposed to do in a separating equilibrium, namely guessing a certain state of the world when not receiving any signal. A small invasion of senders sending a signal in the other state of the world now suffices to make it a best response for the receivers to act according to a separating equilibrium, so that the proportion of 8 This approach of taking the pooling equilibrium as a starting point is similar to Lewis' (1969) argument that a signaling convention may arise through precedent (as an alternative to the salience explained in Section 1.1). 9 For binary signaling games, Hofbauer and Huttegger (2008)'s analysis shows that the results of Huttegger (2007) and Pawlowitsch (2008) for the twopopulation model, carry over to the one-population model. The precise relation between the dynamics of two-population models and one-population models is analyzed in Cressman (2003, Section 3.4.1). 10 The two interpretations are not incompatible. A player's population of ideas may adapt both to own experience, and the experience of others.

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Table 2 Predictions on equilibrium selection of different theories for our four signaling games. Approach:

Focal point theory

Pooling-based intuitive criterion

Pooling-based evolutionary approach

Sample: Standard Costly Modified Costly Standard Cheap talk Modified Cheap talk

Full sample with and without precedent Separating-I Separating-I No prediction No prediction

Sub-sample with precedent only Separating-I Separating-F No prediction No prediction

Separating-I Separating-F Separating-I Separating-F

receivers acting in this manner will increase. With a costless signal, this suffices for the proportion of senders acting according to this same separating equilibrium to increase. Yet, as independently shown by Huttegger (2007) and by Pawlowitsch (2008),11, this argument does not suffice to predict that only separating equilibria will be played in cheap talk signaling games such as the Standard and Modified Cheap talk signaling game. The problem is that, on top of a pooling equilibrium and the separating equilibria, these games also have uninformative equilibria where the receiver always makes the same guess, but where the sender in each state randomizes in a sufficiently uninformative way between sending a signal and not sending a signal. A small invasion of senders acting according to a separating equilibrium may then not suffice to alter the best response of the receiver.12 Nevertheless, as Huttegger (2007) shows, allowing for evolutionary neutral drift, the population can still escape from such an equilibrium. With costless signals, any signaling strategy is a best response to the senders, so that the sender population may drift towards the pooling equilibrium, after which the appropriate separating equilibrium can again evolve. The evolutionary stability of uninformative equilibria in the Standard and Modified Costly signaling games is studied in De Jaegher (2008). Uninformative equilibria of the type described above do not exist now, but the pooling equilibrium is neutrally stable, because with a costly signal a small invasion of receivers acting according to a separating equilibrium does not suffice to make it a best response for the senders to act according to this same separating equilibrium. Yet, through evolutionary neutral drift, a series of small perturbations can again lead a sufficient proportion of the receivers to act according to a separating equilibrium, so that separating equilibria are again predicted.13 A smaller part of the literature focuses on which separating equilibrium is most likely to be played, if a separating equilibrium does evolve. For the Standard Costly signaling game, Benz et al. (2005) both show analytically that the separating-I equilibrium pairwise risk dominates (Kandori and Rob, 1998) the separating-F equilibrium, and through simulations that the separating-I equilibrium has a larger basin of attraction than the separating-F equilibrium. The reasoning here is that each initial population state is equally likely, so that equilibria with a larger basin of

11 While the focus of Pawlowitsch (2008) lies on games with at least three states and two signals, her result that the signaling system may get trapped in a suboptimal state where one signal is used for two states, resembles the result, for two states of the world and one signal, that players can get trapped in uninformative equilibria. The case of two states of the world is explicitly treated by Huttegger (2007). 12 As shown by Huttegger (2007), an exception is found in variants of our cheap talk games where pF=0.5, in which case such uninformative equilibria do not attract an open set of initial conditions. 13 In Jäger's (2008b) costly signaling model, the number of states, the frequencies of these states, and the costs of the signals are all generic. Allowing for evolutionary drift, he shows that if the number of events exceeds the number of signals, some states are never communicated, and that if the number of signals exceeds the number of states, the most expensive signals are never used.

attraction are more likely to be played.14 Yet, as argued by Huttegger (2007), p. 17), “strategies in which agents do not use any signal and never react to receiving a signal (…) might be considered as a more realistic starting point for an initial population state”.15 Following this argument, in what we here call the pooling-based evolutionary approach, one always takes the pooling equilibrium where the sender does not send any signal and where the receiver always makes the same guess, as an initial population state, and looks at which separating equilibrium can evolve from this population state through evolutionary neutral drift.16 Taking this approach, De Jaegher (2008), focusing on binary signaling games, shows that in the Standard (respectively Modified) Costly signaling game, only the separating-I (respectively separating-F) equilibrium can evolve through drift. In the Standard (Modified) Costly signaling game, in the pooling equilibrium the receiver guesses F (I) after not receiving a signal. Through evolutionary neutral drift, he can now plan to do I (F) when receiving the signal. As soon as a sufficient number of receivers act in this manner, the separating-I (separating-F) equilibrium evolves. We add here that this argument does not depend on the cost of the signal, so that in exactly the same manner, the separating-I equilibrium is predicted to evolve in the Standard Cheap talk signaling game, and the separating-F equilibrium in the Modified Cheap talk signaling game. For a summary of these predictions, see Table 2 in Section 2.2, Column 3. Note that these predictions focus on the most likely outcome of the learning process, and not on the learning process itself: given that we cannot observe the population of ideas in players' minds, we can also not observe how the population of ideas evolves. This fits the focus of the predictions of focal point theory and of the pooling-based intuitive criterion, which concern the predicted outcome, and not how players form focal points, or how they reason when receiving a signal though they expected to play a pooling equilibrium.

2. Methods 2.1. Design In our experiment, we administered the four signaling games reported in Table 1 with the payoffs summarized in Fig. 1. Each time, the frequent state occurred with probability 0.75. For the two Standard signaling games, we set the participants' payoffs 14 It can be checked that in the Modified Costly signaling game, again the separating-I equilibrium pairwise risk dominates the separating-F equilibrium, which in turn pairwise risk dominates the pooling equilibrium. In both the Standard and the Modified Cheap talk signaling game, the separating equilibria pairwise risk dominate the pooling equilibrium, while there is no dominance relationship between the two separating equilibria. 15 In the same manner, biologists studying animal signaling have taken as an initial condition an ancestral condition without signaling (see e.g. RodriguezGirones et al. (1996); Bergstrom and Lachmann (1997)). 16 A related idea is found in Gilboa and Matsui's (1991) concept of accessibility. A strategy profile is accessible from another strategy profile if under best-response dynamics a dynamic path exists from the former to the latter.

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K. De Jaegher et al. / Journal of Theoretical Biology 363 (2014) 62–73 F

4 –c, 4

I

x –c , x

when a correct guess was made equal to 4, and the payoff when a wrong guess was made equal to –11, such that for any participant maximizing expected payoff without knowledge of the states, it was better to guess the frequent state (0.75  4þ 0.25  (–11) 40.75  (–11) þ0.25  4). In the two Modified signaling games, guessing I always lead to payoff 1, whereas guessing F correctly lead to payoff 4 and guessing F incorrectly to payoff –11. In the two costly signaling games, the cost of signaling was 2, whereas in the two cheap talk signaling games this cost was zero. In a typical signaling treatment, the computer first announced the subject's role (sender or receiver). Each sender was then randomly and anonymously matched to a receiver. Next, in a partner design, the participants played against the same player throughout the treatment, fitting the focus of focal point theory and of the pooling-based intuitive criterion on coordination between individual sender–receiver pairs. At the beginning of each round, the sender (but not the receiver) was informed, which of two possible states (labeled ‘U’ and ‘D’) the computer had randomly drawn at the level of their pair, where the incidence of these states was common knowledge. In a direct response design, the sender then had to choose whether or not to send a single available signal to the receiver by clicking on the corresponding option on the computer screen (indicated as “send signal” and “no signal”).17 After the sender's decision, the receiver observed the sender's choice (“Your partner decided to send/not to send you a signal”), and then had to guess which of the two states had been drawn by the computer (by clicking on either a ‘U’ or a ‘D’ on the computer screen). Finally, the original random draw of the computer, the sender's and receiver's action taken, and the payoff corresponding to this action, were announced to each participant before the next round began. The game was played for 20 rounds per treatment. Multiple rounds were implemented in the first place to make sure that a sufficient number of states U and D is observed, thus making separating equilibria observable; at the same time, multiple rounds allow learning to take place within individual sender–receiver pairs.18 It is important to note that, during the whole experiment, participants were not able to communicate in natural language or in any other way with each other, except by means of the described signal, through the

computer. Moreover, the signal did not have a pre-given, commonly-known meaning. As explained in Sections 1.2 and 1.3, both pooling-based theories assume that players take as a starting point a primordial state without signaling, where a pooling equilibrium is automatically played. In the lab, in treatments where we make it possible for senders to send a signal, the pooling equilibrium is not necessarily the starting point, as senders may immediately try to play a separating equilibrium. Moreover, even if players do initially play a pooling equilibrium, it is difficult to observe that they do this: if a sender starts out by not signaling, this may be because she intends to play a separating equilibrium, but happens to have observed the state where she does not send a signal. For this reason, in four of the eight sessions, we administered a guessing treatment, before administering a particular signaling treatment. Guessing treatments resemble corresponding signaling treatments, except that signaling is incapacitated, so that participants may be seen as being forced to play the pooling equilibrium. In line with the pooling-based intuitive criterion and the poolingbased evolutionary approach, once signaling is allowed, players should be influenced by the guess that was taken in the preceding guessing game, in the absence of a signal. From the viewpoint of the pooling-based evolutionary approach, the receiver should continue to respond to the absence of a signal in the same manner as in the guessing game, but may learn to respond in a different manner when receiving a signal. From the viewpoint of the pooling-based intuitive criterion, if the signal is costly, when receiving a costly signal after having played the guessing game, the receiver should consider what this says about the state which the sender observed. As summarized in Fig. 2, at the beginning of each round of a guessing treatment, participants were informed that the computer had randomly drawn (for each participant separately) one of the two states (labeled U or D), again with a probability of the (in) frequent state of 0.75 (0.25). Each participant was then asked to guess which state the computer had randomly drawn (each participant automatically had the role of the receiver, as there was no sender to send the signal). After each round, the participant received feedback on the true state, the chosen action, and the payoff obtained. In every guessing treatment, the guessing game was repeated for 10 rounds.19 We implemented a Standard guessing game with the payoffs of the Standard signaling games, and a Modified guessing game with the payoffs of the Modified signaling games. For each of the four signaling games, we ran sessions where the signaling treatment was preceded by the corresponding guessing treatment and where it was not. This setup enabled us to test whether previous play of a pooling equilibrium primes participants to play a particular separating equilibrium in the subsequent signaling treatment.20 Summarizing, in the experiment, we have three treatment variables: whether signaling is Costly or Cheap, whether payoffs are as in the Standard games or Modified games, and whether a guessing game was played before the signaling game or not. This implies a 2  2  2 factorial design: each of the four signaling games, once with a guessing game as a precedent and once without. In order to duplicate observations for our treatment

17 An alternative design for our experiment would have been the strategy design, where the sender chooses an encoding and the receiver a decoding strategy (cf. Selten and Warglien, 2007). We chose the direct response design because we wanted to avoid inducing the agents to play a separating equilibrium. 18 As an alternative, in a stranger design, sender–receiver pairs would be randomly re-matched in every round. The advantage of such a design is that population states and learning dynamics could be observed. Yet, each treatment then yields only a single observation, in the form of a single population state at the end of the 20 rounds.

19 As pointed out by Friedman and Sunder (1994), p. 30), because of boredom and fatigue, if we would let the participants play more rounds, they may prefer to change their behavior, just to relieve the tedium. 20 In psycholinguistics, it is commonly known that how language is interpreted in one context (e.g., in the form of spatial expressions, such as in “from London to Paris”) primes its interpretation in another context (in the form of temporal expressions, such as in “from Monday to Friday”). For an overview, see Rosenbach and Jäger (2008), who point out that evolutionary game theory has little to say about how language learning takes place, and argue that priming fills this gap.

Receiver Send signal Sender

F Don’t send signal

F p = 0.75 Computer

(1 – p ) = 0.25

Send signal

I Sender Don’t send signal Receiver

4, 4

I

x, x

F

–11– c, –11

I

y – c, y

F

–11,–11

I

y, y

Fig. 1. Signaling games. Costly signaling games: c ¼2; cheap-talk signaling games: c ¼0; standard signaling games: x¼ –11, y¼ 4; and modified signaling games: x¼ y¼ 1.

K. De Jaegher et al. / Journal of Theoretical Biology 363 (2014) 62–73

F

4

Participant

F

I

x

p F = 0.75 Computer

–11 (1 – p F) = 0.25

F

I

I y Fig. 2. Guessing games. Standard guessing game: x ¼–11, y¼4; and modified guessing game: x ¼y ¼1.

Table 3 Frequencies of strategies (in percent) per treatment, averaged over periods and sessions.

Separating-F Separating-I Pooling Failure

Standard Costly

Standard Cheap

Modified Costly

Modified Cheap

10.09 80.00nnn 1.78 8.12

34.38 55.15nnn 0.00 9.46

14.33 75.42nnn 0.00 10.26

37.28 52.02nnn 0.00 10.70

n,nn,nnn indicate respectively po 0.1,o0.05, o 0.01 for T-test and Wilcoxon ranksum test. Tests compare frequencies of separating-I with separating-F.

variables, we administered four treatments per session, following a classical cross-over design (see Table A1 in Appendix A). At the end of the experiment subjects were asked to fill in a questionnaire registering general demographic variables. We ran eight sessions at the experimental laboratory ELSE at Utrecht University (see Table 3 for the sessions). The initial sessions (Sessions 1– 6) were run on 10 and 11 December 2007, two sessions (Sessions 7 and 8) were run on 4 June 2008 in the same laboratory. All sessions were computerized, using z-tree (Fischbacher, 2007).21 Each session involved 18–20 participants, 150 in total. No subject participated in more than one session. The participating subjects came from a subject pool with more than 1400 active, registered students from all faculties of the Utrecht University. On average, a subject was 22 years old. The experiment lasted about 90 min and subjects obtained an average payoff of €15.44 (with a maximum of €20.77 and a minimum of €8.96). 2.2. Hypotheses Table 2 summarizes the predictions of the theories reviewed in the subsections of Section 1. Ideally, each theory predicts a specific equilibrium for each game. Yet, focal point theory only provides us with predictions for the costly signaling games. The predictions are valid for treatments with and without immediately preceding play of a specific pooling equilibrium (i.e., the respective guessing treatment as precedent). For the cheap talk signaling games focal 21 The experimental instructions that were handed out to the participants and screen shots from the experimental program are available on request.

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point theory does not allow us to select among the three possible equilibria. The two pooling-based theories on the other hand only provide us with predictions for treatments with immediately preceding play of a specific pooling equilibrium, while they do not say anything for treatments without such a precedent. For the sub-sample of treatments with a precedent the pooling-based evolutionary approach provides us with predictions for all signaling games, while the pooling-based intuitive criterion only provide us with predictions for the costly signaling games. We therefore base our hypotheses on the predictions for two samples, on the one hand the full sample, not differentiated according to whether there was preceding play of a guessing game, and on the other hand the sub-samples of treatments with preceding play of a guessing game only, to specifically address the predictions of the pooling-based theories.22 For the Standard and the Modified Costly signaling game, as is clear from Table 2, Column 1, focal point theory allows us to make the following prediction about the frequency with which either the separating-I or the separating-F equilibrium is played in the full sample: H1. In the full sample the separating-I equilibrium is predominantly played in the Standard Costly signaling game as well as in the Modified Costly signaling game. Following Table 2, Columns 2 and 3, both the pooling-based evolutionary approach and the pooling-based intuitive criterion allow us to formulate the following hypotheses about the subsamples with precedent only: H2a. In the sub-sample with immediately preceding play of the Standard guessing game the separating-I equilibrium is predominantly played in the Standard Costly signaling game. H2b. In the sub-sample with immediately preceding play of the Modified guessing game the separating-F equilibrium is predominantly played in the Modified Costly signaling game. As (H2a) and (H2b) do not allow us to discriminate between the two pooling-based theories, we formulate equivalent hypotheses (H3a) and (H3b) for the two cheap talk signaling games, which are able to discriminate the pooling-based evolutionary approach (Table 2, Columns 2 and 3): H3a. In the sub-sample with immediately preceding play of the Standard guessing game the separating-I equilibrium is predominantly played in the Standard Cheap signaling game. H3b. In the sub-sample with immediately preceding play of the Modified guessing game the separating-F equilibrium is predominantly played in the Modified Cheap signaling game. If the effect of preceding play of the pooling equilibrium is as predicted by the pooling-based evolutionary approach, then forced initial play of the pooling equilibrium as implemented by the guessing treatment, should increase the likelihood of the predictions made in Table 2, Column 3, compared to the corresponding treatment without preceding play. That is, immediately preceding play should increase the likelihood of playing the separating-I equilibrium (separating-F equilibrium) in the Standard Cheap signaling games (Modified Cheap signaling games). This leads us to formulate hypotheses (H4a) and (H4b). 22 An apparent problem is that the evolutionary approach models a population of players who are repeatedly and randomly matched to play the signaling game, while in our experiment the same pairs of senders and receivers repeatedly play the game. Yet, as shown by Börgers and Sarin (1997), the population states of the evolutionary approach may be interpreted as a “population of ideas” in the mind of the individual participant who slowly adapts his or her strategies according to some learning dynamic. It is this interpretation that we follow when using the pooling-based evolutionary approach to formulate hypotheses.

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H4a. Immediately preceding play of the Standard guessing game increases the likelihood that the separating-I equilibrium is played in the Standard Cheap talk signaling game. H4b. Immediately preceding play of the Modified guessing game increases the likelihood that the separating-F equilibrium is played in the Modified Cheap talk signaling game. Finding similar effects for the costly signaling games would allow us to discriminate both pooling-based theories from focal point theory. For completeness we therefore also formulate hypotheses (H5a) and (H5b). H5a. Immediately preceding play of the Standard guessing game increases the likelihood that the separating-I equilibrium is played in the Standard Costly signaling game. H5b. Immediately preceding play of the Modified guessing game increases the likelihood that the separating-F equilibrium is played in the Modified Costly signaling game.

3. Results 3.1. Identification of strategies In order to test the hypotheses we first need to identify the strategies in the data. To do this, we start with a very strict criterion by requiring consecutive play of a strategy over the entire sequence of 20 periods.23 Hence, for the identification of the separating-I equilibrium or the separating-F equilibrium we require faultless sending and interpreting of signals in all 20 periods. For identifying a pooling equilibrium we require that the sender either always sent the signal or never sent it, and that the receiver always guessed the frequent, respectively the infrequent state. All remaining sender and receiver behavior is coded as “Failure”. Using this coding procedure, Fig. 3 shows, for each signaling game over the full sample, the absolute frequency with which the sender and the receiver coordinated on different equilibria.24 Fig. 3 shows that at least 39.29% (22 pairs in the Standard Cheap talk signaling game) and at most 57.2% (32 pairs in the Standard Costly signaling game) of all subjects successfully played the separating equilibrium by either playing the separating-I equilibrium or the separating-F equilibrium in all 20 periods. The separating-I equilibrium was played most often while the pooling equilibrium was played least often, which for the costly signaling games is consistent with Horn's rule.25 Fig. 3 also shows that a majority of participants played the separating-I equilibrium more frequently in the costly signaling games, and that “Failure” is relatively more frequent in the cheap talk signaling games. It is important to note that the data underlying Fig. 3 is the full sample. Therefore, although the comparatively high frequency of the separating-I equilibrium provides first support for Hypothesis (H1), it does not allow any inference for hypotheses (H2a) to (H5b) as the latter are based on sub-samples with immediately preceding play of a (corresponding) guessing game. The definition of equilibrium strategies in Fig. 3 is very demanding with respect to the theory, as a single mistake in the course of 23 We also require that the infrequent state occurred at least once in the 20 periods, which was always the case. 24 As all Standard signaling games were administered equally often and in the same sessions as Modified signaling games (see Table A1 in Appendix A), the reported frequencies are directly comparable within and across these two game types. 25 There was no case of a pooling equilibrium in which the sender sent a signal over all 20 periods, and also no case of an uninformative equilibrium where the sender mixed to send the signal in an uninformative way, and the receiver always chose the infrequent or the frequent state respectively.

the 20 periods or even a switch of strategies is already coded as coordination failure. This hides close-to-equilibrium or more complicated equilibrium play that may produce quite different results. In a second step, we therefore identify strategies in each period separately. This approach allows for the switching of strategies and occasional mis-coordination, but has the drawback that it is not possible to detect a pooling equilibrium. At the period level, when detecting behavior that is not consistent with a separating equilibrium, we cannot be sure whether this is a coordination mistake or part of a long-term pooling strategy. Therefore, before identifying the other strategies per period, we first coded the sender–receiver pairs that played the pooling equilibrium over the entire range of 20 periods. At the period level, we do not report these pairs under the category “Failure”, but under “Pooling”. From Fig. 3 we know that only 1.78% of all pairs play pooling.26 For the remaining pairs, we record how often per period both subjects in the randomly matched pairs decided in accordance with the separating-I or the separatingF equilibrium. Fig. 4 presents the average frequencies of the strategies per period (as a percentage of all decisions in that period, averaged over sessions) for the full samples (not the sub-samples) (we stress that the labels separating-I and separating-F mean that individual participants play, in the given round, in accordance with the equilibria with these same labels, but do not imply that pairs of participants coordinate on such equilibria). Interestingly, the frequencies are quite consistent over time, which indicates that equilibrium play is relatively stable. As immediately preceding play of the guessing game is an important element in our design and hypotheses tests, we also check subjects' behavior in these guessing games. Fig. 5 reports the frequencies with which actions I and F were played over all 10 periods of the Standard guessing game and the Modified guessing game. In the Standard guessing game, as predicted, players predominantly play F. In the Modified guessing game, the expected value of playing I is larger. Accordingly, most players play I, although a large portion also plays F.27 Importantly, majority play in the Modified guessing game (majority plays I) differs from majority play in the Standard guessing game (majority plays F). This enables us to test whether previous play of a specific pooling equilibrium has an effect on the type of separating equilibrium that is played thereafter. 3.2. Hypotheses testing To test Hypothesis (H1) we analyze the frequencies with which participants coordinated on the separating-I equilibrium in the full sample of the Standard Costly and the Modified Costly signaling game. In Section 3.1, Fig. 3 showed that the separating-I equilibrium was played most frequently in all signaling games. This provides support for (H1) when strategies are defined over the entire range of 20 periods. 26 As a robustness check, we alternatively considered the frequency of different strategies for ranges of 5 periods (available upon request). To be able to identify the strategies, we require again at least one occurrence of the infrequent state within this sequence of 5 periods. In case there was no such occurrence of both states within the 5 periods under consideration, strategies are undetermined, because they at the same time corresponded to both a separating equilibrium and a pooling equilibrium. The frequency with which the pooling equilibria is played over 5 periods is equally low as over 20 periods (below 2% of all pairs). Thus, coding the pairs that play pooling over the entire range of 20 periods as “Pooling” in our analysis at the period level does not seem to bias our results. 27 In (unreported) robustness checks we find that the large portion of subjects playing F can be explained by the so-called gambler's fallacy, which can itself be explained by Tversky and Kahneman's (1974) representativeness heuristic of boundedly rational decision makers facing uncertainty. After having observed the F-state for three periods (which, statistically, about half of the players do in Periods 1 to 3), many players expect the I-state for the next period, even though the probability that the I-state occurs in any period always is 1/4.

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Fig. 5. Frequency of actions F and I in the guessing games (in percent) per period and treatment, averaged over sessions. Fig. 3. Frequencies of strategies per treatment over all 20 periods.

Fig. 4. Frequencies of strategies (in percent) per period and treatment, averaged over sessions.

When identifying and analyzing strategies per period, we need to complement the graphical comparisons in Fig. 4 (Section 3.1) with two-sample tests on the equality of frequency distributions for different strategies, averaged over periods and sessions, for all four signaling games. In all two-sample analyses we use both the Student's t-test and the Wilcoxon rank-sum test (a.k.a. Mann Whitney test statistic) and report statistical levels of significance at p o0.1, p o0.05 and p o0.01. Table 3 reports the average frequency of equilibrium play per period and the results of the above-mentioned statistical tests on the equality of means and distributions. In confirmation of (H1), the Standard Costly signaling game as well as in the Modified Costly signaling game the separating-I equilibrium was played more often than all other strategies. The difference is economically and statistically highly significant (p o0.01). This finding is in accordance with focal point theory. Note that in the full sample the separating-I equilibrium was also played more frequently in the

cheap talk signaling games. A possible explanation for this will be discussed at the end of this section. Hypotheses (H2a) and (H2b) predict that in treatments with immediately preceding play of the Standard (Modified) guessing game the separating-I (separating-F) equilibrium should predominantly be played in the Standard (Modified) Costly signaling game. Table 4 reports the average frequencies per period for all signaling treatments that were played at the beginning of a session or that followed the corresponding guessing games at the beginning of the session (i.e., Standard Costly signaling game in Sessions 1 and 7, Modified Costly signaling game in Sessions 2 and 4, Standard Cheap talk signaling game in Sessions 3 and 5, and Modified Cheap talk signaling game in Sessions 6 and 8, respectively).28 Table 4 shows that, after playing the corresponding guessing game, in the Standard Costly signaling game the separating-I equilibrium is played in 77.78% of all cases, while the separatingF equilibrium is played only in 0.56%. In the Modified Costly signaling game with immediately preceding play of the Modified guessing game (precedent: yes) the separating-F equilibrium is played, on average, in 35% of all cases, while the separating-I equilibrium is played in 59.44%. All of these differences are statistically significant at po 0.01. While the first finding confirms (H2a) and is consistent with all three theories, (H2b) is rejected and contradicts the two pooling-based theories. We next look at play in the Cheap talk signaling games, i.e. at Hypotheses (H3a) and (H3b), in the sub-sample for which play was preceded by a corresponding guessing game. As shown in Table 4, in the Standard Cheap talk signaling game with the immediately preceding play of the Standard guessing game the separating-I equilibrium is played in 68.75% of all cases (precedent: yes), while the separating-F equilibrium is played in 0.00%. In the Modified Cheap talk signaling game with the immediately preceding play of the Modified guessing game the separating-F equilibrium is played in 70% of all cases, the separating-I equilibrium is played in 19%. Again, all differences are statistically significant at p o0.01. These findings confirm (H3a) and (H3b) and are consistent only with the pooling-based evolutionary approach.29

28 We focus on these subsamples to ensure that the effect of the guessing game is free of potentially confounding effects of preceding play of another signaling treatment. In fact, we find that guessing games played later in the sequence of treatments (e.g. Treatments 3 in Sessions 1 and 2, or Treatments 3 in Sessions 5 and 6) did not have a strong enough priming effect on subsequent signaling games to overrule the priming effect of previous signaling treatments in the same session. 29 All results mentioned here are robust if we define strategies not per period, but as equilibrium play over the whole range of 20 periods as presented in Fig. 3.

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Table 4 Frequencies of separating equilibria (in percent) per treatment, with and without preceding play of a Guessing game, averaged over periods and sessions. Game type

Standard Costly Standard Cheap Modified Costly Modified Cheap n,nn,nnn

Separating-I

Separating-F

Precedent: yes1

Precedent: no2

Yes–no3

Precedent: yes1

Precedent: no2

Yes–no3

77.78nnn 68.75nnn 59.44nnn 19.00nnn

83.89 20.00nnn 73.00 41.11

 6.11nnn 48.75  13.56nnn  22.11

0.56nnn 0.00nnn 35.00nnn 70.00nnn

6.67nn 62.5nn 13.50 37.78nn

 6.11nnn  62.50 21.50nnn 32.22

indicate respectively po 0.1, po 0.05, p o 0.01.

1

T-test and Wilcoxon rank-sum test comparing data for Separating-I (with precedent) to data for Separating-F (with precedent). 2 Random effects logistic estimations with a dummy for Separating-I/-F as dependent. Asterisks indicate statistical significance of a precedent-dummy as explanatory variable. Detailed estimations in Appendix. 3 T-test and Wilcoxon rank-sum test comparing differences in frequencies (with and without precedence) of a costly signaling game type with the differences of the respective cheap talk signaling game type.

To address Hypotheses (H4a) and (H4b) we compare the average frequency of playing a specific separating equilibrium in the cheap talk signaling games with precedent of a corresponding guessing game, to the average frequency in these same games without precedent. To test for such a precedence effect we run logistic regressions with a dummy (equal 1, else 0) for the hypothesized separating equilibrium as dependent variable and, as explanatory variable, a dummy (equal 1, else 0) if a guessing game was played before the signaling game. We control for period effects, subjects' age (in years), gender (dummy female equal 1, else 0), origin (dummy foreign equal 1, else 0), and a dummy (equal one) for participants with friends in the lab. All standard errors are estimated with random effects at the sender–receiver pair level and are heteroskedasticity-consistent. The statistical significance of the precedence dummy is reported in Table 4 (with asterisks), together with the average frequencies of playing a specific separating equilibrium. (More detailed estimation results are reported in Table A2 in Appendix A.) Table 4 shows that the immediately preceding play of the Standard guessing game increases the likelihood that the separating-I equilibrium is played in the Standard Cheap talk signaling game from 20% (precedent: no) to 68.75% (precedent: yes). This precedence effect is statistically significant (p o0.01), as indicated by corresponding asterisks in the second column for separating-I in Table 4 (and in the first column in Table A2). This result confirms (H4a) and is consistent with the pooling-based evolutionary approach. Further, in the spirit of (H4a), the separating-F equilibrium is played less often when the Standard Cheap talk signaling game is preceded by the Standard guessing game. In fact, as shown in Table 4, the average frequency decreases from 62.5% to 0% and this decrease is also statistically significant (p o0.05) as indicated for the separating-F equilibrium in Table 4 (and in the second column in Table A2). For the Modified Cheap talk signaling game, immediately preceding play of the Modified guessing games increases the likelihood that the separating-F equilibrium is played. In line with the pooling-based evolutionary approach, (H4b) is confirmed, as the difference is statistically significant (p o0.05). Hypotheses (H5a) and (H5b) formulate similar effects for the costly signaling games. As reported in Table 4 (and in Table A2), we do not find a precedence effect for the separating-I equilibrium in the Standard Costly or the Modified Costly signaling games. Yet, with respect to playing the separating-F equilibrium, the immediately preceding play of the Standard guessing game does have a statistically significant negative effect (p o0.05) in the Standard Costly signaling game. This effect is in the spirit of (H5a) and is consistent with both the pooling-based intuitive criterion and the pooling-based evolutionary approach, and shows that focal point

theory is not the only theory explaining behavior of our participants in the costly signaling variants.30 From a more explorative perspective, and without further hypotheses, we use the data to elaborate on the relative importance of the precedence effect, by comparing the differences in frequencies with and without precedent of a guessing game across the two samples of costly and cheap talk signaling games. Table 4 reports the average differences within each sample and the statistical significance of twosample tests across costly and cheap talk signaling games. As reported in Table 4, in the third column of separating-I and separating-F, respectively, we find that the average effect of a precedent is systematically larger for cheap signaling games. This applies to a two-sample comparison of the Standard Costly with the Standard Cheap talk signaling game (po0.01), as well as the Modified Costly with the Modified Cheap talk signaling game (po0.01). Overall, the comparison of the frequencies of separating equilibria in the costly signaling games is more in line with focal point theory than with the pooling-based evolutionary approach or with the pooling-based intuitive criterion. We find some indication for a precedence effect on costly signaling games, which is consistent with both the pooling-based intuitive criterion and the poolingbased evolutionary approach. Yet, we also find significant effects of a preceding guessing game on the cheap talk signaling games, which is more consistent with the pooling-based evolutionary approach than with the pooling-based intuitive criterion.31 Moreover, the effects of a preceding guessing game are economically and statistically stronger for the cheap talk signaling games than for the costly signaling games. Hence, a precedence effect in line with the pooling-based evolutionary approach does exist in our experiment, but it does not override efficiency as a focal point,

30 All of the reported logistic estimation results for Hypotheses (H4a) to (H5b) are qualitatively robust to univariate comparisons of the respective frequencies (averages) in Table 4 with two sided t-tests and Wilcoxon tests. 31 This is in line with the ambiguous results of laboratory experiments on forward induction arguments such as the intuitive criterion (see Brandts and Holt (1992); an overview is contained in Brandts et al. (2007), Section 3). Brandts and Holt design a variant of the Beer-Quiche game (Cho and Kreps, 1987) where participants learn to play an equilibrium which violates the intuitive criterion. Their participants seem to do this because they respond to out-of-equilibrium moves by looking at the circumstances in which such moves occurred in earlier rounds, and not because of deductive reasoning about incentives for such deviations from equilibrium, as predicted by the intuitive criterion. For similar, more recent results, see Anderson and Camerer (2000) and Cooper and Kagel (2009). Our experiment differs in two aspects. First, initial conditions are induced by play in preceding guessing games, and not by play in the initial rounds of the signaling games. Second, we do not create tension between play induced by initial conditions and play induced by the intuitive criterion. Instead, in our Modified Costly signaling game, we create tension between play induced by initial conditions and the intuitive criterion on the one hand, and by payoff dominance on the other hand.

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when costs are present. This is particularly apparent in the Modified Costly signaling game with preceding play of a guessing game and the unsupported Hypotheses (H2b) and (H5b). In our design we cannot observe the population of ideas as this population exists only in the minds of the sender and the receiver in an individual sender–receiver pair. However, to investigate how important learning is for our participants we can look at how strategies change from the first to the last round in each treatment. For the Standard Costly signaling game we find that the frequency of coordination increases by 25 percentage points, from 73.21% of all decisions to 98.21%. This also applies to the Modified Costly signaling game with an increase of 15.87 percentage points from 71.23% to 87.10%, to the Standard Cheap talk signaling game with an increase of 32.46 percentage points from 64.03% to 96.49%, and to the Modified Cheap talk signaling game with an increase of 24.56 percentage points from 68.42% to 92.98%. The difference in learning between the cheap talk and the costly signaling treatments is statistically significant with p=0.0638 using a t-test (paired, one-sided), suggesting that more learning is taking place in the cheap talk than in the costly signaling treatments.32 This is in line with our result above that the precedence effect is more dominant in the cheap talk than in the costly signaling treatments. When comparing average frequencies of strategies in the full sample as reported in Table 3, participants predominantly play the separating-I equilibrium also in the cheap talk signaling games. This effect is particularly prominent in treatments of the cheap talk signaling games that followed treatments of the costly signaling games earlier in the same session. In fact, in the second half of Sessions 4 and 7, the separating-I equilibrium was played in the Standard (Modified) Cheap talk signaling game in, on average, 81.48% (79.21%) of all sender–receiver decisions. This stands in stark contrast to the first half of Sessions 3 and 8, where an average of only 41.05% (30.79%) of all sender–receiver decisions in the Standard (Modified) Cheap talk game were in accordance with the separating-I equilibrium. Although not explicitly addressed in the subsections of Section 1, this observation does not contradict any of the three theories. We cannot exclude that, after the separating-I equilibrium became a focal point in a previous costly signaling game (because of its efficiency), it continues to be focal in an ensuing cheap talk signaling game. Further, if participants have previously played the separating-I equilibrium in a costly signaling game, then the evolutionary approach predicts, and the intuitive criterion does not contradict, the continuation of the separating-I equilibrium in the cheap talk signaling games.

4. Discussion Our experiment considers a simple signaling game with a frequent and an infrequent state of the world. When a single costly signal without a pre-given meaning is available, our participants predominantly coordinate on the efficient separating equilibrium where the costly signal is sent in the infrequent state (also referred to as Horn's rule), rather than on the inefficient separating equilibrium where the costly signal is sent in the frequent state. The fact that the signal is costly seems to represent a focal point and suggests that communication is based on economic principles rather than being conventional. This conclusion is corroborated by treatments where the signaling game is preceded by a game where signaling is incapacitated, so that participants are forced to initially play the pooling equilibrium. In 32 In the two sample t-test we compare 16 changes in the coordination frequency in costly signaling games (8 modified costly and 8 standard costly) with 16 changes in cheap talk signaling games (8 modified cheap and 8 standard cheap talk).

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particular, we consider a variant of the signaling game where payoffs are modified in such a way that in the pooling equilibrium, it is optimal for receivers to guess the infrequent state. One would expect that this primes receivers to guess the infrequent state when they do not receive a signal, in accordance with the inefficient separating equilibrium, in an immediately following signaling game. Yet, we find that even in this case participants coordinate on the efficient separating equilibrium, giving further credence to the argument that economic use of the costly signal serves as a focal point. However, we also provide weak support for the intuitive criterion and evolutionary game theory as competing explanations by comparing treatments of the signaling game with and without immediately preceding play of an equivalent game with incapacitated signaling. Our data show that such a precedent significantly decreases the likelihood of the inefficient separating equilibrium in the subsequent signaling game. This effect is in line with both the intuitive criterion and evolutionary game theory. These indications for a precedence effect are interesting: while in our experiment the cost of the signal is particularly salient (the cost of the signal is one of our main treatment variables), in real life efficiency may often be less salient, and in such cases precedence effects may be more pronounced. Finally, we also consider treatments where the signal is costless. Here, participants predominantly coordinate on signaling in the infrequent (frequent) state in games without (with) modified payoffs, when these are preceded by an equivalent game with incapacitated signaling. These precedence effects are significantly larger in games with costless signals (compared with costly signals). As the intuitive criterion applies only when the signal is costly, these results are in support of evolutionary game theory. They also suggest that the latter theory explains our observation of a precedence effect in the costly signaling game, where we cannot discriminate between the intuitive criterion and evolutionary game theory. It should be stressed that we have only tested whether the equilibria which our participants seem to play in a binary signaling game, are in accordance with either focal point theory, with the pooling-based intuitive criterion, or with the pooling-based evolutionary argument, where we have formulated variants of our basic signaling game for which these three theories predict different equilibria. We have not tested if and how participants form focal points, if and how they reason in accordance with forward induction, or if and how they learn to play specific equilibria. Answering each of these three questions requires a separately designed signaling experiment. We end by noting that the cost of signals is only one manner in which economic principles can be relevant for communication (De Jaegher and Van Rooij, 2014). When signals differ according to their levels of noise, it is efficient to relegate the use of the more noisy signals to states of the world where such noise has less impact. The same applies to the case when fewer signals are available than there are states of the world: here, for some states of the world precision may be more important than for other states of the world. The question whether players can also coordinate on efficient separating equilibria in these cases, provides an interesting avenue for future research. Acknowledgments We would like to thank two anonymous referees, Robert van Rooij, Michael Franke, and participants of the 24th Annual Congress of the European Economics Association for helpful comments. Any remaining errors are our own. Appendix A See Tables A1 and A2.

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Table A1 Sequence of treatments (see Figs. 1 and 2) in eight sessions. Session

Treatment 1

Treatment 2

Treatment 3

Treatment 4

1 2 3 4 5 6 7 8

Standard Modified Standard Modified Standard Modified Standard Modified

Standard Modified Modified Standard Standard Modified Modified Standard

Modified Standard Standard Modified Modified Standard Standard Modified

Modified Standard Modified Standard Modified Standard Modified Standard

guessing guessing cheap costly guessing guessing costly cheap

costly costly cheap costly cheap cheap costly cheap

guessing guessing costly cheap guessing guessing cheap costly

costly costly costly cheap cheap cheap cheap costly

Table A2 Random effects logistic estimation of precedence effects. Game type

Standard Cheap

Dependent

Separ.-I

Separ.-F

Separ.-I

Separ.-F

Separ.-I

Separ.-F

Separ.-I

Separ.-F

Precedent

2.746nnn [2.784] 0.02 [1.535] 0.048 [0.347] 1.008 [0.873] 0.806 [0.678]  1.584n [  1.891]  3.603 [  1.390]

 2.201nn [  2.091] 0.028 [1.628]  0.016 [  0.125]  0.382 [  0.453]  1.116 [  1.038] 1.208 [1.483] 1.045 [0.383]

 1.255 [  1.268] 0.041n [1.882]  0.136n [  1.750] 0.567 [0.831] Dropped Dropped  0.864 [  0.976] 1.925n [1.717]

2.018nn [2.482] 0.050nn [2.267] 0.083 [1.287]  1.122 [  1.633] 3.185nnn [3.954] 0.413 [0.524]  3.140nn [  2.572]

0.816 [1.036] 0.080n [1.896]  0.043 [  1.639]  0.042 [  0.084] 0.059 [0.116]  1.237nnn [  2.983] 2.215nn [2.076]

 2.962nn [  2.355] 0.083 [0.970] 0.056 [1.378] 0.029 [0.037]  0.669 [  0.744] 1.297n [1.953]  5.240nnn [  3.446]

 0.56 [  0.631] 0.034 [1.337] 0.071 [0.934] 0.146 [0.225]  1.441n [  1.840]  0.27 [  0.314]  0.514 [  0.274]

1.104 [1.095]  0.003 [  0.128]  0.099 [  1.002]  0.768 [  1.155] 1.019 [1.441] 0.523 [0.494] 0.415 [0.151]

720 15.349 0.26 0.018

720 27.631 0.176 0

760 9.723 0.107 0.083

760 32.327 0.298 0

720 25.09 0.079 0

720 16.235 0.172 0.013

760 8.716 0.084 0.19

760 9.05 0.109 0.171

Period Age Female Foreign Friends in lab Constant # Obs. Wald χ2 McFadden's R2 prob4χ2

Modified Cheap

Standard Costly

Modified Costly

Note: Odds ratios with t-values in parenthesis; heteroskedasticity-consistent estimator of variance; random effects at sender–receiver pair level. ‘Foreign’ dropped in H4b as it predicts failure perfectly. n

po 0.1. p o0.05. nnn p o0.01. nn

References Anderson, C.M., Camerer, C.T., 2000. Experience-weighted attraction learning in sender–receiver signaling games. Econ. Theory 16, 689–718. Benz, A., Jäger, G., van Rooij, R., 2005. An introduction to game theory for linguists. In: Benz, A., Jäger, G., Rooij, R. van (Eds.), Game Theory and Pragmatics. Palgrave Macmillan, London, pp. 1–83. Bergstrom, C.T., Lachmann, M., 1997. Signaling among relatives I. Is costly signaling too costly? Philos. Trans. R. Soc. B: Biol. Sci. 352, 609–617. Blume, A., DeJong, D.V., Kim, Y.-K., Sprinkle, G.B., 1998. Experimental evidence on the evolution of meaning of messages in sender–receiver games. Am. Econ. Rev. 88, 1323–1340. Blume, A., DeJong, D.V., Kim, Y.-G., Sprinkle, G.B., 2001. Evolution of communication with partial common interest. Games Econ. Behav. 37, 79–120. Blume, A., Kim, Y.-G., Sobel, J., 1993. Evolutionary stability in games of communication. Games Econ. Behav. 5, 547–575. Börgers, T., Sarin, R., 1997. Learning through reinforcement and replicator dynamics. J. Econ. Theory 77, 1–14. Brandts, J., Cabrales, A., Charness, C., 2007. Forward induction and entry deterrence: an experiment. Econ. Theory 33, 183–209. Brandts, J., Holt, C.A., 1992. An experimental test of equilibrium dominance in signaling games. Am. Econ. Rev. 82, 1350–1365. Cai, H., Wang, J.T.-Y., 2006. Overcommunication in strategic information transmission games. Games Econ. Behav. 56, 7–36. Cho, I.K., Kreps, D., 1987. Signaling games and stable equilibria. Q. J. Econ. 102, 179–222. Cooper, D.J., Kagel, J.H., 2009. Equilibrium selection in signaling games with teams: forward induction or faster adaptive learning? Res. Econ. 63, 216–224. Crawford, V.P., 1998. A survey of experiments on communication via cheap talk. J. Econ. Theory 78, 286–298.

Crawford, V.P., Sobel, J., 1982. Strategic information transmission. Econometrica 50, 1431–1451. Crémer, J., Garicano, L., Prat, A., 2007. Language and the theory of the firm. Q. J. Econ. 122, 373–407. Cressman, R., 2003. Evolutionary Dynamics and Extensive Form Games. MIT Press, Cambridge, MA. De Jaegher, K., 2008. The evolution of Horn's rule. J. Econ. Methodol. 15, 275–284. De Jaegher, K., van Rooij, R., 2014. Game-theoretic pragmatics under conflicting and common interests. Erkenntnis 79, 769–820. Dos Santos, M., Rodrigues, J.F.M., Wedekind, C., Ranking, D.J., 2012. The establishment of communication systems depends on the scale of competition. Evol. Hum. Behav. 33, 232–240. Farrell, J., 1993. Meaning and credibility in cheap-talk games. Games Econ. Behav. 5, 514–531. Fischbacher, U., 2007. z-Tree: Zurich toolbox for ready-made economic experiments. Exp. Econ. 10, 171–178. Friedman, D., Sunder, S., 1994. Experimental Methods: A Primer for Economists. Cambridge University Press, Cambridge, MA. Fudenberg, D., Tirole, J., 1991. Perfect Bayesian equilibrium and sequential equilibrium. J. Econ. Theory 53, 236–260. Fudenberg, D., Tirole, J., 1993. Game Theory. MIT Press, Cambridge, MA. Galantucci, B., 2009. Experimental semiotics: a new approach for studying communication as a form of joint action. Top. Cogn. Sci. 1, 393–410. Gilboa, I., Matsui, A., 1991. Social stability and equilibrium. Econometrica 58, 859–867. Grice, H.P., 1975. Logic and conversation. In: Cole, P., Morgan, J. (Eds.), Syntax and Semantics 3: Speech Acts. Academic Press, New York, pp. 41–58. De Haan, T. Offerman T., Sloof, R., 2011. Money talks? An empirical investigation of cheap talk and burned money. Tinbergen Institute Discussion Paper TI 2011 – 069/1.

K. De Jaegher et al. / Journal of Theoretical Biology 363 (2014) 62–73

Hillas, J., Kohlberg, E., 2002. Conceptual foundations of strategic equilibrium. In: Aumann, S., Hart, S. (Eds.), Handbook of Game Theory, III. Elsevier, New York, pp. 1597–1663. Hofbauer, J., Huttegger, S.M., 2008. Feasibility of communication in binary signaling games. J. Theor. Biol. 254, 843–849. Horn, L., 1984. Towards a new taxonomy of pragmatic inference: Q-based and Rbased implicature. In: Schiffrin, D. (Ed.), Meaning, Form, and Use in Context: Linguistic Applications GURT84. Georgetown University Press, Washington, pp. 11–42. Huttegger, S.M., 2007. Evolution and the explanation of meaning. Philos. Sci. 74, 1–27. Huttegger, S.M., Zollman, K.J.S., 2011. Signaling games: dynamics of evolution and learning. In: Benz, A., Ebert, C., Jäger, G., Rooij, R. van (Eds.), Language, Games, and Evolution. Springer-Verlag, Berlin, pp. 160–176. Jäger, G., 2008a. Applications of game theory in linguistics. Lang. Linguist. Compass 2/3, 406–421. Jäger, G., 2008b. Evolutionary stability conditions for signaling games with costly signals. J. Theor. Biol. 253, 131–141. Kandori, M., Rob, R., 1998. Bandwagon effects and long run technology choice. Games Econ. Behav. 22, 30–60. Lewis, D., 1969. Convention: A Philosophical Study. Harvard University Press, Cambridg,e MA. Martinet, A., 1955. Economie des changements phonétiques. Traité de phonologie diachronique. Francke, Bern. Noveck, I.A., Reboul, A., 2008. Experimental pragmatics: a Gricean turn in the study of language. Trends Cogn. Sci. 12, 425–431. Nowak, M.A., Krakauer, D.C., 1999. The evolution of language. Proc. Natl. Acad. Sci. 96, 8028–8033. Parikh, P., 1991. Communication and strategic inference. Linguist. Philos. 14, 473–513. Parikh, P., 2000. Communication, meaning, and interpretation. Linguist. Philos. 23, 185–212.

73

Parikh, P., 2001. The Use of Language. CSLI Publications, Stanford. Pawlowitsch, C., 2008. Why evolution does not always lead to an optimal signaling system. Games Econ. Behav. 63, 203–226. Van Rooij, R., 2004. Signalling games select Horn strategies. Linguist. Philos. 27, 493–527. Van Rooij, R., 2008. Games and quantity implicatures. J. Econ. Methodol. 15, 261–274. Rodriguez-Girones, M.A., Cotton, P.A., Kacelnik, A., 1996. The evolution of begging: signaling and sibling competition. Proc. Natl. Acad. Sci 93, 14637–14641. Rosenbach, A., Jäger, G., 2008. Priming and unidirectional language change. Working paper. Sally, D., 2005. Can I say “bobobo” and mean “There's no such thing as cheap talk”? J. Econ. Behav. Organ. 57, 245–266. Sánchez-Pagés, S., Vorsatz, M., 2007. An experimental study of truth-telling in a sender–receiver game. Games Econ. Behav. 61, 86–112. De Saussure, F., 1983. Course in General Linguistics (trans. Roy Harris). Duckworth, London (1916). Schelling, T., 1960. The Strategy of Conflict. Oxford University Press, New York. Schlag, K., 1998. Why imitate, and if so how? A boundedly rational approach to multi-armed bandits. J. Econ. Theory 78, 130–156. Selten, R., Warglien, M., 2007. The emergence of simple languages in an experimental coordination game. Proc. Natl. Acad. Sci. 104, 7361–7366. Spence, M., 1973. Job market signaling. Q. J. Econ. 87, 355–374. Tversky, A., Kahneman, D., 1974. Judgment under uncertainty: heuristics and biases. Science 185, 1124–1131. Wärneryd, K., 1993. Cheap talk, coordination and evolutionary stability. Games Econ. Behav. 5, 532–546. Zahavi, A., 1975. Mate selection – a selection for a handicap. J. Theor. Biol. 53, 205–214. Zipf, G.K., 1949. Human Behavior and the Principle of Least Effort. Addison-Wesley Press, Cambridge, MA.