Perturbed communication games with honest senders and naive receivers

This paper studies communication games in which the sender is possibly honest (tells the truth) and the receiver is possibly naive (follows messages as if truthful). The characterization of message-monotone equilibria in the perturbed games explain several important aspects of strategic communication including sender exaggeration, receiver skepticism and message clustering. Surprisingly, the strategic receiver may respond to more aggressive claims with more moderate actions. In the limit as the probabilities of the non-strategic players approach zero, (i) the limit equilibrium corresponds to a most-informative equilibrium of the limit (Crawford-Sobel) game; (ii) only the top messages are sent.     

Between-game rule learning in dissimilar symmetric normal-form games

Rule learning posits that decision makers, rather than choosing over actions, choose over behavioral rules with different levels of sophistication. Rules are reinforced over time based on their historically observed payoffs in a given game. Past works on rule learning have shown that when playing a single game over a number of rounds, players can learn to form sophisticated beliefs about others. Here we are interested in learning that occurs between games where the set of actions is not directly comparable from one game to the next. We study a sequence of ten thrice-played dissimilar games. Using experimental data, we find that our rule learning model captures the ability of players to learn to reason across games. However, this learning appears different from within-game rule learning as previously documented. The main adjustment in sophistication occurs by switching from non-belief-based strategies to belief-based strategies. The sophistication of the beliefs themselves increases only slightly over time.     

A folk theorem for repeated games played on a network

I consider repeated games on a network where players interact and communicate with their neighbors. At each stage, players choose actions and exchange private messages with their neighbors. The payoff of a player depends only on his own action and on the actions of his neighbors. At the end of each stage, a player is only informed of his payoff and of the messages he received from his neighbors. Payoffs are assumed to be sensitive to unilateral deviations. The main result is to establish a necessary and sufficient condition on the network for a Nash folk theorem to hold, for any such payoff function.     

Trading with a common agent under complete information: A characterization of Nash equilibria

We analyze an abstract model of trading where N principals submit quantity-payment schedules that describe the contracts they offer to an agent, and the agent then chooses how much to trade with every principal. This represents a special class of common agency games with complete information. We study all the subgame perfect Nash equilibria of these games, not only truthful ones, providing a complete characterization of equilibrium payoffs. In particular, we show that the equilibrium that is Pareto-dominant for the principals is not truthful when there are more than two of them. We also provide a partial characterization of equilibrium strategies.     

Coordination with communication under oath

We focus on the design of an institutional device aimed to foster coordination through communication. We explore whether the social psychology theory of commitment, implemented via a truth-telling oath, can reduce coordination failure. Using a classic coordination game, we ask all players to sign voluntarily a truth-telling oath before playing the game with cheap talk communication. Three results emerge with commitment under oath: (1) coordination increased by nearly 50%; (2) senders’ messages were significantly more truthful and actions more efficient, and (3) receivers’ trust of messages increased.     

A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.     

Markov Perfect Equilibrium: I. Observable Actions

We define Markov strategy and Markov perfect equilibrium (MPE) for games with observable actions. Informally, a Markov strategy depends only on payoff-relevant past events. More precisely, it is measurable with respect to the coarsest partition of histories for which, if all other players use measurable strategies, each player's decision-problem is also measurable. For many games, this definition is equivalent to a simple affine invariance condition. We also show that an MPE is generically robust: if payoffs of a generic game are perturbed, there exists an almost Markovian equilibrium in the perturbed game near the initial MPE. Journal of Economic Literature Classification Numbers: C72, C73.     

Sampling equilibrium, with an application to strategic voting

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.     

Risk attitudes and the stag-hunt game

A stag-hunt game (with the risky and safe actions) has two pure Nash equilibria that are Pareto-rankable. The risky action leads either to the Pareto-superior equilibrium (high payoff) or to out of equilibrium (low payoff) depending on the opponent’s action. Both players may want to obtain high payoff but uncertainty about the opponent’s action may prevent them to take such strategic risk. This paper investigates how information about the risk attitude of an opponent affects a player’s action choice in the stag-hunt game. I find that although a subject’s propensity to choose the risky action depends on her opponent’s risk attitude, it does not depend on her own risk attitude.     

Words, Deeds, and Lies: Strategic Behaviour in Games with Multiple Signals

We report the results of an experiment in which subjects play games against changing opponents. In one treatment, "senders" send "receivers" messages indicating intended actions in that round, and receivers observe senders' previous-round actions (when matched with another receiver). In another treatment, the receiver additionally observes the sender's previous-round message to the previous opponent, enabling him to determine whether the sender had lied. We find that allowing multiple signals leads to better outcomes when signals are aligned (all pointing to the same action), but worse outcomes when signals are crossed . Also, senders' signals tend to be truthful, though the degree of truthfulness depends on the game and treatment, and receivers' behaviour combines elements of pay-off maximization and reciprocity.     

Selecting equilibria in common agency games

We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one restricts out-of-equilibrium behavior in a natural way, the refinement is effective. Alternatively, we may consider an exponential distribution with unbounded support (and hence no out-of-equilibrium choices) and we find that the refinement selects a unique equilibrium payoff vector equal to Lindahl prices.As a separate contribution, equilibria with forcing contracts are also considered both under complete and asymmetric information.     

Mechanism design with multidimensional, continuous types and interdependent valuations

We consider the mechanism design problem when agents’ types are multidimensional and continuous, and their valuations are interdependent. If there are at least three agents whose types satisfy a weak correlation condition, then for any decision rule and any ?>0 there exist balanced transfers that render truthful revelation a Bayesian ?-equilibrium. A slightly stronger correlation condition ensures that there exist balanced transfers that induce a Bayesian Nash equilibrium in which agents’ strategies are nearly truthful.     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.     

Aggregate information cascades

We introduce a new model of aggregate information cascades where only one of two possible actions is observable to others. Agents make a binary decision in sequence. The order is random and agents are not aware of their own position in the sequence. When called upon, they are only informed about the total number of others who have chosen the observable action before them. This informational structure arises naturally in many applications. Our most important result is that only one type of cascade arises in equilibrium, the aggregate cascade on the observable action. A cascade on the unobservable action never arises.     

One-Shot Public Mediated Talk

We show that any correlation device with rational coefficients can be generated by a mechanism, where each player sends a private message to a mediator who in turn makes a public deterministic announcement. It is then shown that the mechanism can be adapted also to situations with differential information, where the correlation device itself depends on the players' private messages that may vary with their realized types. All the mechanisms suggested are immunized against individual deviations. Therefore, by using them, players can implement any correlated or communication equilibrium.Journal of Economic LiteratureClassification Number: C72.     

Delay and information aggregation in stopping games with private information

We consider equilibrium timing decisions in a model with a large number of players and informational externalities. The players have private information about a common payoff parameter that determines the optimal time to invest. They learn from each other in real time by observing past investment decisions. We develop new methods of analysis for such large games, and we give a full characterization of symmetric equilibria. We show that the equilibrium statistical inferences are based on an exponential learning model. Although the beliefs converge to truth, learning takes place too late. Ex-ante welfare is strictly between that without observational learning and that with full information.     

INCOMPLETE INFORMATION GAMES WITH MULTIPLE PRIORS*

We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player “updates” his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. We define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players’ views on uncertainty about the environment affect the strategic outcomes.     

Ambiguity,data and preferences for information – A case-based approach

We model decision making under ambiguity based on available data. Decision makers express preferences over actions and data sets. We derive an α-max–min representation of preferences, in which beliefs combine objective characteristics of the data (number and frequency of observations) with subjective features of the decision maker (similarity of observations and perceived ambiguity). We identify the subjectively perceived ambiguity and separate it into ambiguity due to a limited number of observations and ambiguity due to data heterogeneity. The special case of no ambiguity provides a behavioral foundation for beliefs as similarity-weighted frequencies as in Billot et al. (2005) [3].     

Extinction in common property resource models: an analytically tractable example

We discuss an analytically tractable discrete-time dynamic game in which a finite number of players extract a renewable resource. We characterize a symmetric Markov-perfect Nash equilibrium of this game and derive a necessary and sufficient condition under which the resource does not become extinct in equilibrium. This condition requires that the intrinsic growth rate of the resource exceeds a certain threshold value that depends on the number of players and on their time-preference rates.     

A detail-free mediator

We present a cheap talk extension to any two-player, finite, complete information game, and ask what correlations over actions are implementable in Nash equilibria of the extended game. In the extension, players communicate repeatedly through a detail-free mediator that has been studied in Lehrer (1991) and in Gossner and Vieille (2001). The extension captures situations in which people can observe the opponentʼs face during the conversation. While Gossner and Vieille (2001) prove that no correlation can be securely implemented by using only this mediator, we prove a result closer to Lehrer (1991), namely, that the Nash equilibrium payoffs of the extended game essentially coincide with the correlated equilibrium payoffs of the underlying game. The contrasting results can be explained with our additional assumptions that the players can also communicate directly and, more importantly, the private messages sent to the mediator can be recorded and revealed later in the conversation.