We show that the use of communications to coordinate equilibria generates a Nash-threats folk theorem in two-player games with “almost public†information. The results generalize to the <i>n</i>-person case. However, the two-person case is more difficult because it is not possible to sustain...

Forecasts are said to be calibrated if the frequency predictions are approximately correct. This is a refinement of an idea first introduced by David Blackwell in 1955. We show that “<i>K</i>-initialized myopic strategies†are approximately calibrated when <i>K</i> is large. These strategies first...

Players choose an action before learning an outcome chosen according to an unknown and history-dependent stochastic rule. Procedures that categorize outcomes, and use a randomized variation on fictitious play within each category are studied. These procedures are “conditionally...

We examine games played by a single large player and a large number of opponents who are small, but not anonymous. If the play of the small players is observed with noise, and if the number of actions the large player controls is bounded as the number of small players grows, the equilibrium set...

We study a variation of fictitious play, in which the probability of each action is an exponential function of that action's utility against the historical frequency of opponents' play. Regardless of the opponents' strategies, the utility received by an agent using this rule is nearly the best...

We comment on the Shoham, Powers, and Grenager survey of multi-agent learning and game theory, emphasizing that some of their categories are important for economics and others are not. We also try to correct some minor imprecisions in their discussion of the economics literature on learning in...

We provide a necessary and sufficient condition for equilibria of a game to arise as limits of ε-equilibria of games with smaller strategy spaces. As the smaller games are frequently more tractable, our result facilitates the characterization of the set of equilibria.

In a self-confirming equilibrium, each player correctly forecasts the actions that opponents will take along the equilibrium path, but may be mistaken about the way that opponents would respond to deviations. This paper develops a refinement of self-confirming equilibrium in which players use...

This paper discusses the implications of learning theory for the analysis of games with a move by Nature. One goal is to illuminate the issues that arise when modeling situations where players are learning about the distribution of Nature's move as well as learning about the opponents'...

We argue that some, but not all, superstitions can persist when learning is rational and players are patient, and illustrate our argument with an example inspired by the Code of Hammurabi. The code specified an “appeal by surviving in the river†as a way of deciding whether an...