In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive structure. More precisely, I construct a...

This paper studies repeated games with imperfect private monitoring when there exists a third-party mediator who coordinates play by giving non-binding instructions to players on which action to take and by collecting their private information. The paper presents a Nash-threat folk theorem for a...

A model of repeated price competition with large buyers is analyzed. The sellers are allowed to offer different prices to different buyers and the buyers act strategically. The set of subgame perfect Equilibria is investigated under public and private monitoring. With public monitoring the...

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...

A fundamental non-stationarity of infinitely repeated games as usually studied is that the length of the history of play gets longer each period. With private actions (and mixed strategies) or private signals, this introduces a particular difficulty with common solution concepts such as...

This paper proposes and studies a tractable subset of Nash equilibria, belief-free review-strategy equilibria, in repeated games with private monitoring. The payoff set of this class of equilibria is characterized in the limit as the discount factor converges to one for games where players...

I study two-player undiscounted repeated games with imperfect private monitoring. When strategies are restricted to those implementable by nite automata, fewer equilibrium outcomes are possible. When only two-state automata are allowed, a simple strategy, "Win-Stay, Lose-Shift," leads to...

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,...

There is a large repeated games literature illustrating how future interactions provide incentives for cooperation. Much of this literature assumes public monitoring: players always observe precisely the same thing. Even slight deviations from public monitoring to private monitoring that...