Cheap Talk Equilibria Research Articles

Bayesian persuasion: Reduced form approach

We introduce reduced form representations of Bayesian persuasion problems where the variables are the probabilities that the receiver takes each of her actions. These are simpler objects than, say, the joint distribution over states and actions in the obedience formulation of the persuasion problem. This can make a difference in computational and analytical tractability, which we illustrate with two applications. The first shows that with quadratic receiver payoffs, the worst-case complexity scales with the number of actions and not the number of states. If |A| and |S| denote the number of actions and states respectively, the worst case complexity of the obedience formulation is O(|A||S|(|S|+|A|)1.5L) where L is its input size. The worst-case complexity of the reduced form representation is O(|A|2.5L). In the second application, the reduced form leads to a simple greedy algorithm to determine the maximum value a sender can achieve in any cheap talk equilibrium.

Reference dependent prices in bargaining: An experimental examination of precise first offers

Evidence from psychology and marketing suggests that those who make a “precise” first offer in bargaining get a better deal than those who make a “round” first offer. We report on a series of experiments designed to test for and improve our understanding of the “precise first offer” (PFO) effect in bargaining and whether it likely reflects rational optimizing or equilibrium behavior. Our experiment varies whether decisions are incentivized and whether the PFO effect can emerge as an equilibrium of a cheap-talk signaling game. We find evidence of a PFO effect when subjects read a vignette and make unincentivized individual decisions. When monetary incentives are added to the vignette, we still find the PFO effect, but it is not robust. In a bilateral bargaining situation with a cheap-talk equilibrium, we can not find the PFO effect, which is inconsistent with the equilibrium predictions. Moreover, the PFO effect reemerges in a setting in which initial offers are generated by a random device and thus provides a strong refutation of the signaling model. Our evidence suggests that optimizing and equilibrium accounts of the PFO effect are inadequate. Understanding initial offers as reference points, which subtly change perceptions about the kinds of acceptable counteroffers, provides a plausible account of a new finding on which prior explanations are silent: precise offers induce more precise counteroffers.

The (non-)robustness of influential cheap talk equilibria when the sender\u2019s preferences are state independent

Chakraborty and Harbaugh (Am Econ Rev 100(5):2361–2382, 2010) prove the existence of influential cheap talk equilibria in one sender one receiver games when the state is multidimensional and the preferences of the sender are state independent. We show that influential equilibria do not survive the introduction of any small degree of Harsanyi-uncertainty, i.e., uncertainty about the sender’s preferences in the spirit of Harsanyi (Int J Game Theory 2(1):1–23, 1973).

Reference Dependent Prices in Bargaining: An Experimental Examination of Precise First Offers

Evidence from psychology and marketing suggests that those who make a first in bargaining get a better deal than those who make a round first offer. We report on a series of experiments designed to test for and improve our understanding of the first offer (PFO) effect in bargaining and whether it likely reflects rational optimizing or equilibrium behavior. Our experiment varies whether decisions are incentivized and whether the PFO effect can emerge as an equilibrium of a cheap-talk signaling game. We find evidence of a PFO effect when subjects read a vignette and make unincentivized individual decisions. When monetary incentives are added to the vignette, we still find the PFO effect, but it is not robust. In a bilateral bargaining situation with a cheap-talk equilibrium, we can not find the PFO effect, which is inconsistent with the equilibrium predictions. Moreover, the PFO effect reemerges in a setting in which initial offers are generated by a random device and thus provides a strong refutation of the signaling model. Our evidence suggests that optimizing and equilibrium accounts of the PFO effect are inadequate. Understanding initial offers as reference points, which subtly change perceptions about the kinds of acceptable counteroffers, provides a plausible account of a new finding on which prior explanations are silent: precise offers induce more precise counteroffers.

Should the Talk be Cheap in Contribution Games?

AbstractThis paper studies the equilibria of contribution games with commitment and with cheap talk under incomplete information. When agents contribute to a club good, we find that with commitment, high types contribute early to induce low types to contribute in later rounds. With cheap talk, low types signal to contribute early but may drop out later if they find the total contributions are low. When there are sufficiently many rounds, we construct a cheap talk equilibrium that implements the ex-post efficient and ex-post individually rational allocation. In contrast, every equilibrium of the commitment game is inefficient. When the good is a public good, the cheap-talk game admits no informative equilibria. In this case, the equilibria of the commitment game may be more efficient.

Communication under language barriers

We study the welfare effect of language barriers in communication. Specifically, we compare the equilibrium welfare in a game with language barriers to that in the equivalent game without language barriers. We show how and why language barriers may (weakly) improve welfare by providing two positive results. First, in a game with any language barriers, we prove that if we allow for N-dimensional communication, any equilibrium outcome of the equivalent game without language barriers can be replicated. Second, for any payoff primitive, we provide a welfare ranking for several noisy-communication devices, including language barriers, that generalizes the results in Goltsman et al. (2009). In particular, our results imply that there always exist some language barriers whose maximal equilibrium welfare (always weakly and sometimes strictly) dominates any noisy-talk equilibrium (and hence also any cheap-talk equilibrium) under no language barriers.

Meaning and credibility in experimental cheap-talk games

We design experimental games to evaluate the predictive power of the first cheap‐talk refinement, neologism‐proofness. In our first set of treatments designed to evaluate the refinement with its usual emphasis on literal meanings, we find that a fully revealing equilibrium that is neologism‐proof is played more often; senders deviate from an equilibrium in a way that can be predicted by the credibility of the neologism; and receivers' behavior indicates that they understand senders' deviating incentives. Our second set of treatments evaluates neologism‐proofness from an evolutionary perspective in the absence of a common language. We find that the proportion of observations in which the meaning of a neologism evolves to disrupt a prevailing fully revealing equilibrium is lower when the equilibrium is neologism‐proof. Our findings shed light on the capabilities and limitations of the refinement concept in predicting laboratory behavior under different language environments. Neologism‐proofness cheap talk equilibrium refinement evolution of meanings laboratory experiment C72 C92 D82 D83

Transparency is Overrated: Communicating in a Coordination Game with Private Information

We consider an experiment with a version of the Battle of the Sexes game with two-sided private information, allowing a possible round of either one-way or two-way cheap talk before the game is played. We compare different treatments to study truthful revelation of information and subsequent payoffs from the game. We find that the players are overall truthful about their types in the cheap-talk phase in both one-way or two-way talk. Furthermore, the unique symmetric cheap-talk equilibrium in the two-way cheap talk game is played when they players fully reveal their information; however, they achieve higher payoffs in the game when the talk is one-way as the truthful reports facilitate desired coordination.

Beneficial mediated communication in cheap talk

This paper investigates mediated communication between an informed sender and an uninformed receiver with conflicting preferences in the framework of Crawford and Sobel (1982). It provides a simple condition for mediation to be beneficial, that is, to give the receiver a higher ex-ante payoff than the uninformed decision. This condition in turn allows us to identify scenarios in which mediation is beneficial while all cheap-talk equilibria are uninformative. Our condition extends the conditions for beneficial mediation with a binary type space (Mitusch and Strausz, 2005) and mediation via a biased mediator (Ambrus et al., 2013). Finally, we show the connection between the identified condition and related conditions in other conflict resolution schemes: delegation (Alonso and Matouschek, 2008) and arbitration (Kovác and Mylovanov, 2009).

For those about to talk we salute you: an experimental study of credible deviations and ACDC

We test the Average Credible Deviation Criterion (ACDC), a stability measure and refinement for cheap talk equilibria introduced in De Groot Ruiz et al. (Equilibrium selection in cheap talk games: ACDC rocks when other criteria remain silent, Working paper, University of Amsterdam 2012a). ACDC has been shown to be predictive under general conditions and to organize data well in previous experiments meant to test other concepts. In a new experimental setting, we provide the first systematic test of whether and to which degree credible deviations matter for the stability of cheap talk equilibria. Our principal experimental result is that in a setting where existing concepts are silent, credible deviations matter and matter gradually, as predicted by ACDC.

An Optimal Signaling Equilibrium

This paper analyses the optimal combination of costly and costless messages that a Sender uses in a signaling game if he is able to choose among all equilibrium communication strategies. We provide a complete characterization of the equilibrium that maximizes the Sender's ex ante expected utility in case of uniformly distributed types and quadratic loss functions. First, the Sender often wants to avoid money burning by using the most informative cheap talk communication strategy. Second, if he does burn money, he avoids separation and only re-arranges the existing intervals of the most informative cheap talk equilibrium, possibly adding one extra interval. Money burning takes place in the second interval only.

Self-enforced collusion through comparative cheap talk in simultaneous auctions with entry

Campbell (J Econ Theory 82:425–450, 1998) develops a self-enforced collusion mechanism in simultaneous auctions based on complete comparative cheap talk and endogenous entry, with two bidders. His result is difficult to generalize to an arbitrary number of bidders, since the entry-decision stage of the game is characterized by strategic substitutes. This paper analyzes more-than-two-bidder, symmetric-prior cases. Two results are proved: (1) as the number of objects grows large, a full comparative cheap talk equilibrium exists and it yields asymptotically fully efficient collusion; and (2) there is always a partial comparative cheap talk equilibrium. All these results are supported by intuitive equilibria at the entry-decision stage (J Econ Theory 130:205–219, 2006; Math Soc Sci 2008, forthcoming). Numerical examples suggest that full comparative cheap talk equilibria are not uncommon even with few objects.

Cheap Talk, Status Quo and Delegation

The paper analyzes a communication game between a decision-maker and a reputationally concerned expert drawn from a population of informed and uninformed experts. It departs from the literature [e.g. (Ottaviani and Sorensen(2006), Scharfstein and Stein (1990)] by considering the possibility that some of the decision-maker's actions may not reveal the true state of the world. This is shown to change the equilibria of cheap talk games significantly. Experts' strategies get intertwined with the decision-maker's action choice even if these actions have no payoff implications for experts. This leads to different types of equilibria for decision-makers with different payoff functions. Among other things, it opens up the possibility of strategic delegation of the game by one decision-maker to another. It is shown that such delegation allows the original decision-maker to achieve the maximum possible payoff sustainable in a cheap talk equilibrium.

Cheap Talk and Bogus Network Externalities in the Emerging Technology Market

Many emerging technologies exhibit path-dependent demands driven by positive network feedback. Such network effects profoundly impact marketing strategists' thinking in today's network economy. However, the significant network externalities expected by many people often fail to materialize in the emerging technology market. We analyze this phenomenon in the context of a technology distribution channel. By studying cheap-talk strategies under information asymmetry, we show that incentive-compatible contracts are essential for achieving credible information transmission. In our model, the better-informed technology vendor has an incentive to inflate the retailer's ex ante belief of network externalities when a wholesale price contract is adopted. When properly termed revenue-sharing contracts are implemented, there are information-efficient cheap-talk equilibria where truthful information transmission is mutually beneficial. When the vendor's information is imperfect, even revenue-sharing contracts cannot guarantee credible information transmission if there is significant prior belief disparity between the vendor and the retailer. This study demonstrates how information-inefficient equilibria (e.g., information blockage) arise because of the conflict of interest or the conflict of opinion among channel members. It also explores the role of cheap talk in facilitating channel coordination.

Rich language and refinements of cheap-talk equilibria

I formalize the notion of equilibrium language, define the relation of having a richer language, and show the existence of equilibria with maximally rich language. I also study the stability of equilibria with respect to inflows of messages that can enrich their language, and provide examples of implausible cheap-talk equilibria, not refined away by the existing refinements, which can be refined away on the grounds of stability properties.

Communication and Courtship: Cheap Talk Economics and the Law of Contract Formation

This paper provides an extended introduction to the game theoretic analysis of cheap talk -- actions which do not have a direct cost, but which affect equilibria only indirectly, via the information about sender type which they convey. After introducing these games, the article takes a functional approach to the law of contract formation as determining when talk is cheap (when an unfulfilled assurance will not trigger liability) versus when it is not (when an unfulfilled assurance that trade will take place triggers liability for the failure to trade). Using the neologism-proof equlibrium refinement due to Farrell, it is shown that when there is no liability, the unique stable equilibrium with pretrade cheap talk may be informative. Parties may communicate information even when talk is cheap because both parties have an interest in terminating costly negotiations if there is too low a probability that a deal will eventually be struck. There also exist situations in which cheap talk will be uninformative or concealing, because one party is able to externalize a large share of the cost of negotiating to the other, and the other will not bear that cost if it knows that the probability of trade is actually quite low. The article discusses the general structural factors -- such as market thickness, bargaining power, and the similarity between sender and receiver types -- which determine whether there is a (stable) informative cheap talk equilibrium. It then points out that legal rules which attempt to fix liability based on a court's ex post perception of whether talk was concealing or informative ex ante are unlikely to improve matters. On this basis, it is argued that the default rule for letters of intent and other preliminary argreements should be that such agreements do not bind either party to trade. The very well developed law of the United States Court of Appeals for the Second Circuit on this topic is then explicated and critiqued. Other issues such as whether a communication is an offer or an offer solicitation and promissory estoppel in the preliminary dealings context are also explored. In particular, the analysis points out that while efficiency of the the classic Hoffman v. Red Owl is much more debatable than previously assumed, as actually applied by courts today, promissory estoppel in this context may be surprisingly efficient.

Coordination in Auctions with Entry

We examine self-enforcing bidder coordination in auctions in which bidding is costly. Conditions on the distribution of valuations are identified that guarantee multiple equilibria. Under slightly stronger conditions, within the set of “sunspot” payoffs only those that are convex combinations of payoffs of extreme asymmetric equilibria are interim efficient for the bidders. If preplay communication is possible, every no-communication equilibrium payoff is interim Pareto-dominated for the bidders by some cheap-talk equilibrium payoff. When the number of auctions is large, communication equilibria exist that yield ex-post efficient payoffs for the bidders almost surely.Journal of Economic LiteratureClassification Numbers: D44, D82.

Can the Government Talk Cheap? Communication, Announcements, and Cheap Talk

A great deal of attention has recently been focused on communication in economic contexts. While some models of credible announcements have been based on reputational forces or penalties imposed by third parties, as in Sobel [21] and Cothren [4], several recent papers have addressed the possibility of communication through talk, that is, talk in situations with no explicit penalties for deception. Perhaps the most prominent application of cheap talk in the literature is the recent model of Federal Reserve announcements by Stein [22].' This paper will show that cheap talk equilibria of the sort modeled by Stein and others often depend in a fundamental way on implausible discontinuities in public responses to government announcements. That is, cheap talk equilibria are frequently only possible if certain infinitesimally small changes in government announcements are capable of causing large, discontinuous changes in public expectations and behavior. Intuitively, if public expectations are a continuous function of government announcements, then the government can tune these expectations. The government will therefore often be tempted to deviate from the cheap talk equilibrium announcements in order to manipulate expectations. This causes the equilibrium to unravel. Discontinuous public reactions sometimes prevent these equilibria from unraveling because they convert continuous choice problems, which allow manipulative fine tuning, into discrete choice problems, where such fine tuning is impossible. These discontinuities are implausible, however, and this may often rule out cheap talk as a realistic model of governmental policy announcements.2

Cheap talk can matter in bargaining

This paper describes an intuitive way in which cheap talk can matter in a twostage bargaining game in which talk may be followed by serious negotiation. The intuition that all buyers would claim to have low reservation prices is incorrect in our model. Instead, if good-faith participation is endogenously determined then the parties can use talk to trade off bargaining position against the probability of continued negotiation. Our cheap-talk equilibrium features bargaining behavior that could not be equilibrium behavior in the absence of talk.