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In the Crawford–Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of the N possible elements of a partition to the mediator and then the mediator suggests one of the N actions to the uninformed decision-maker according to the probability distribution of the device. We show that no such simple mediated equilibrium can improve upon the unmediated N-partition Crawford–Sobel equilibrium when the preference divergence parameter (bias) is small.

We provide a full characterisation of the set of trading equilibria (in which all goods are traded at a positive price) in a strategic market game (as introduced by Shapley and Shubik),for both the "buy and sell" and the "buy or sell" versions of this model under standard assumptions on the utility functions.We also interpret and illustrate our main equilibrium-characterising condition, using simple examples.

We consider an experiment with a version of the Battle of the Sexes game with two-sided private information, preceded by a round of either one-way or two-way cheap talk. 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 and two-way talk. Furthermore, the unique symmetric cheap-talk equilibrium in the two-way cheap talk game is played when the 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.

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.

We consider the set-up of a Japanese-English auction with exogenously fixed discrete bid levels for the wallet game with two bidders. We prove that bidding twice the signal - the equilibrium strategy with continuous bid levels - is never an equilibrium in this set up. We show that partition equilibria exist that may be separating or pooling. We illustrate some separating and pooling equilibria with two and three discrete bid levels; we also compare the revenues of the seller from these equilibria and thereby find the optimal bid levels in these cases.

We consider a Bayesian game, namely the Battle of the Sexes with private information, in which each player has two types, High and Low. We allow cheap talk regarding players' types before the game and prove that the unique fully revealing symmetric cheap talk equilibrium exists for a low range of prior probability of the High-type. This equilibrium has a desirable type-coordination property: it fully coordinates on the ex-post efficient pure Nash equilibrium when the players' types are different. Type-coordination is also obtained in a partially revealing equilibrium in which only the High-type is not truthful, for a medium range of prior probability of the High-type.

We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibrium.

In this paper we develop tests for whether play in a game is consistent with equilibrium behavior when preferences are unobserved. We provide necessary and sufficient conditions for observed outcomes in extensive game forms to be rationalized first, partially, as a Nash equilibrium and then, fully, as the unique subgame-perfect equilibrium. Thus one could use these conditions to find that play is (a) consistent with subgame-perfect equilibrium, or (b) not consistent with subgame-perfect behavior but is consistent with Nash equilibrium, or (c) consistent with neither. Further, we discuss the relevance of the test outcomes for rationalization of data by multiple preference profiles.

A correlated equilibrium for a normal form game is a mediator whose recommendations the players find optimal to follow obediently. A (direct) correlation device or a mediator however may face the multiple equilibrium problem as the obedient strategy profile may be dominated by some other Nash equilibrium in the extended game. This paper addresses the question whether it is possible to avoid this problem by considering non-canonical correlation devices. The paper presents three different non-canonical correlation devices (one with and two without a sunspot) to understand this problem for a parametric version of the Chicken game.