Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in...

We prove an anti-folk theorem for repeated games with private monitoring. We assume that the strategies have a finite past (they are measurable with respect to finite partitions of past histories), that each period players' preferences over actions are modified by smooth idiosyncratic shocks,...

Side-payments are common in many long-term relationships. We show that when players can exchange side-payments, approximate efficiency is achievable in any repeated game with private monitoring and communication, so long as the players can observe their own payoffs and are sufficiently patient,...

We provide a simple sufficient condition for the existence of a recursive upper bound on (the Pareto frontier of) the sequential equilibrium payoff set at a fixed discount factor in two-player repeated games with imperfect private monitoring. The bounding set is the sequential equilibrium payoff...

We study repeated games in which players learn the unknown state of the world by observing a sequence of noisy private signals. We find that for generic signal distributions, the folk theorem obtains using ex-post equilibria. In our equilibria, players commonly learn the state, that is, the...

This paper provides a model of the repeated prisoner's dilemma in which cheap-talk communication is necessary in order to achieve cooperative outcomes in a long-term relationship. The model is one of complete information. I consider a continuous time repeated prisoner's dilemma game where...

We study the role of communication in repeated games with private monitoring. We first show that without communication, the set of Nash equilibrium payoffs in such games is a subset of the set of ε-coarse correlated equilibrium payoffs (ε-CCE) of the underlying one-shot game. The value of...

This paper extends the framework of Kajii and Morris (1997) to study the question of robustness to incomplete information in repeated games. We show that dynamically robust equilibria can be characterized using a one-shot robustness principle that extends the one-shot deviation principle. Using...

The payoff matrix of a finite stage game is realized randomly, and then the stage game is repeated infinitely. The distribution over states of the world (a state corresponds to a payoff matrix) is commonly known, but players do not observe nature’s choice. Over time, they can learn the state...

We characterize perfect public equilibrium payoffs in dynamic stochastic games, in the case where the length of the period shrinks, but players' rate of time discounting and the transition rate between states remain fixed. We present a meaningful definition of the feasible and individually...