We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a possibly infinitely long (but...

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a...

We extend Aumann's theorem [Aumann 1987], deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker one, joint...

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and...

We present an extension to any finite complete information game with two players. In the extension, players are allowed to communicate directly and, additionally, send private messages to a simple, detail-free mediator, which, in turn, makes public announcements as a deterministic function of...

We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite games with a unique correlated equilibrium is open, while this is not true...

We show on a 4x4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard...

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is equivalent to the set of a version of incomplete information correlated equilibrium which we dub Bayes...

A game of incomplete information can be decomposed into a basic game and an information structure. The basic game defines the set of actions, the set of payoff states the payoff functions and the common prior over the payoff states. The information structure refers to the signals that the...

This paper provides an explicit characterization of correlations that are implicitly captured by partition models for incomplete information games. The main result of this paper shows that every partition model for incomplete information can be decomposed into the conjunctions of a unique...