Cheap talk with multiple audiences: An experimental analysis

We examine strategic information transmission in a controlled laboratory experiment of a cheap talk game with one sender and multiple receivers. We study the change in equilibrium behavior from the addition of another audience as well as from varying the degree of conflict between the senderʼs and receiversʼ preferences. We find that, as in cheap talk games with just one receiver, information transmission is higher in games with a separating equilibrium, than in games with only a babbling equilibrium. More interestingly, we find clear evidence that the addition of another audience alters the communication between the sender and the receiver in a way consistent with the theoretical predictions. There is evidence of the presence of agents that are systematically truthful as senders and trusting as receivers: deviations from the theoretical predictions, however, tend to disappear with experience, and learning is faster precisely in the games where deviations are more pronounced.     

Screening and Signaling in Communication*

In this paper, we analyze a model of repeated strategic communication between a sender and a receiver. The sender has private information on a policy‐relevant variable but does not know the receiver's motives. Together with the desire of the sender to please the receiver and the desire of the receiver to be pleased, the two‐sided incomplete information creates an interesting communication problem in which players can choose to use information strategically. We analyze various modes of communication, which allow for information transmission, and we compare them in terms of both the quality of the policy implemented and the welfare of the players.     

Credulity, lies, and costly talk

This paper studies a model of strategic communication by an informed and upwardly biased sender to one or more receivers. Applications include situations in which (i) it is costly for the sender to misrepresent information, due to legal, technological, or moral constraints, or (ii) receivers may be credulous and blindly believe the sender's recommendation. In contrast to the predictions obtained in the benchmark cheap talk model, our model admits a fully separating equilibrium, provided that the state space is unbounded above. The language used in equilibrium is inflated and naive receivers are deceived.     

Morale,performance and disclosure

We study the optimal disclosure policy in a sender–receiver communication game where the receiver's morale, defined as his expected state of the world, affects his performance. The sender observes the state and chooses whether to disclose it to the receiver, who then decides whether to participate in a task. The receiver wins if his performance in the task meets a target. No disclosure is optimal if the receiver wins with average morale in each state. Otherwise, in the threshold disclosure equilibrium that Pareto-dominates full disclosure, the receiver quits as the sender discloses the worst states and wins as the sender withholds the rest. The receiver wins in more states in the Pareto-optimal equilibrium as the sender chooses a non-monotonic disclosure policy. Our theory reveals a trade-off between transparency and efficiency when morale affects performance. It has applications in a broad range of areas including military, family, education and business.     

Perfect communication equilibria in repeated games with imperfect monitoring

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.     

Value of public information in sender-receiver games

I find in two classes of sender-receiver games that the receiver’s equilibrium payoff is not increasing in the informativeness of a public signal because the sender may transmit less information when the public signal is more informative.     

Enjoy the silence: an experiment on truth-telling

We analyze experimentally two sender–receiver games with conflictive preferences. In the first game, the sender can choose to tell the truth, to lie, or to remain silent. The latter strategy is costly. In the second game, the receiver must decide additionally whether or not to costly punish the sender after having observed the history of the game. We investigate the existence of two kinds of social preferences: lying aversion and preference for truth-telling. In the first game, senders tell the truth more often than predicted by the sequential equilibrium analysis, they remain silent frequently, and there exists a positive correlation between the probability of being truthful and the probability of remaining silent. Our main experimental result for the extended game shows that those subjects who punish the sender with a high probability after being deceived are precisely those who send fewer but more truthful messages. Finally, we solve for the Perfect Bayesian Nash Equilibria of a reduced form of the baseline game with two types of senders. The equilibrium predictions obtained suggest that the observed excessive truth-telling in the baseline game can be explained by lying aversion but not by a preference for truth-telling.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users. Financial support through the Ramón y Cajal program of the Spanish Ministry of Education and Science is gratefully acknowledged. This work was initiated while the author was working at Maastricht University.     

MONEY TALKS? AN EXPERIMENTAL INVESTIGATION OF CHEAP TALK AND BURNED MONEY

We experimentally study the strategic transmission of information in a setting where both cheap talk and money can be used. Theoretically, many equilibria exist side by side, in which senders use either costless messages, money, or both. We find that senders prefer to communicate through costless messages. Only when the interest disalignment between sender and receiver increases does cheap talk tend to break down and high sender types start burning money to enhance the credibility of their costless messages. A behavioral model assuming that sellers bear a cost of lying fits the data best.     

Broadcasting Opinions with an Overconfident Sender*

We analyze a model where an altruistic, but possibly overconfident sender broadcasts one of a finite set of messages to rational receivers. If broadcasting is costless and the sender is rational, there is an informationally efficient equilibrium, but multiple equilibria may arise, and asymmetric equilibria might be more informative than the symmetric equilibrium even if the prior is symmetric. Although overconfidence on the part of the sender reduces informativeness in some cases, it may also eliminate less informative equilibria and lead to better information transmission. Overconfidence can also improve the informativeness of the message when broadcasting is costly.     

Informal communication

The typical sender-receiver game studied in the literature assumes that receiver is uninformed. I analyze a model where receiver has private information and sender cares to be perceived as honest. If sender's honesty concerns are strong enough, the model predicts information revelation as a unique equilibrium. This uniqueness result contrasts with the multiplicity of equilibria in games with uninformed receiver. To achieve information revelation as a unique equilibrium, receiver may have to ask for information, which is extraneous for her decision. If sender's honesty concerns are not too strong, asking for extraneous information may create an incentive for lying.     

A limit characterization of belief-free equilibrium payoffs in repeated games

The present paper studies repeated games with private monitoring, and characterizes the set of belief-free equilibrium payoffs in the limit as the discount factor approaches one and the noise on private information vanishes. Contrary to the conjecture by Ely et al. [J.C. Ely, J. Hörner, W. Olszewski, Belief-free equilibria in repeated games, Econometrica 73 (2005) 377-415], the equilibrium payoff set is computed by the same formula, no matter how many players there are. As an application of this result, a version of the folk theorem is established for N-player prisoner's dilemma games.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Correlated Nash equilibrium

We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler's [I. Gilboa, D. Schmeidler, Maxmin expected utility with nonunique prior, J. Math. Econ. 18 (1989) 141-153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generalization of Nash equilibrium, in the sense that it deviates from Nash equilibrium only in terms of players' attitude towards ambiguity. Consequently, comparing it with Nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played. For example, with ambiguity, (beliefs about) action choices are in general correlated.     

Equilibrium selection in global games with strategic complementarities

We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (Econometrica 61 (1993) 989-1018) for two-player, two-action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.     

Professional advice

This paper studies strategic communication by an expert who is concerned about appearing to be well informed. The expert is assumed to observe a private signal with a simple and particularly tractable (multiplicative linear) structure. The quality of the expert's information is evaluated on the basis of the advice given and the realized state of the world. In equilibrium of this reputational cheap-talk game, no more than two messages are effectively reported. The model is extended to consider sequential communication by experts with conditionally independent signals. In the long run, learning is incomplete and herd behavior arises.     

A Knowledge–based Algorithm for the Internet Transmission Control Protocol (TCP)

Using a knowledge–based approach, the authors derive a protocol for the sequence transmission problem, which provides a high–level model of the Internet transmission control protocol (TCP). The knowledge–based protocol is correct for communication media where deletion and reordering errors may occur. Furthermore, it is shown that both sender and receiver eventually attain depth– n knowledge about the values of the messages for any n , but that common knowledge about the messages is not attainable.     

Harmful lie aversion and lie discovery in noisy expert advice games

This study tests whether individuals are reluctant to tell lies, or perhaps only “harmful lies”, in a previously untested environment: an expert sending a message to a decision maker whose interpretation of that message is subject to error, i.e. a noisy sender–receiver game. In the Aligned treatment, the expert can send a “white lie” to the receiver, eliminating the negative effects of noise and improving both parties’ payoffs. In the Conflict treatment, lies are harmful and the inability to commit to truthtelling destroys all meaningful communication in equilibrium unless there is a cost of lying. In the experiment, receivers are overly trusting and experts learn to take advantage of this. As experts gain experience they tell stronger and more frequent lies in both treatments, consistent with models of reinforcement learning. The findings suggest that neither harmful nor universal lie aversion is a factor when communication is noisy, provided individuals have time to discover their personal benefits of lies.     

Perfect communication equilibria in repeated games with imperfect monitoring

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.     

Cheap talk with two senders and complementary information

This paper studies a cheap talk model in which two senders having partial and non-overlapping private information simultaneously communicate with an uninformed receiver. The sensitivity of the receiverʼs ideal action to one senderʼs private information depends on the other senderʼs private information. We show that the sendersʼ information transmissions exhibit strategic complementarity: more information transmitted by one sender leads to more information being transmitted by the other sender.     

Cheap talk in games with incomplete information

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_i of each player i the expected payoff of t_i in q is larger than the expected payoff of t_i in s.