Private monitoring with infinite histories

This paper develops new recursive methods for studying stationary sequential equilibria in games with private monitoring. We first consider games where play has occurred forever into the past and develop methods for analyzing a large class of stationary strategies, where the main restriction is that the strategy can be represented as a finite automaton. For a subset of this class, strategies which depend only on the players’ signals in the last k periods, these methods allow the construction of all pure strategy equilibria. We then show that each sequential equilibrium in a game with infinite histories defines a correlated equilibrium for a game with a start date and derive simple necessary and sufficient conditions for determining if an arbitrary correlation device yields a correlated equilibrium. This allows, for games with a start date, the construction of all pure strategy sequential equilibria in this subclass.

Stationary consistent equilibrium coalition structures constitute the recursive core

We study coalitional games where the coalitional payoffs depend on the embedding coalition structure. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core, a generalisation of the core to such games. In order to extend past results limited to totally recursive-balanced partition function form games we introduce a more permissive perfectness concept, subgame-consistency that only requires perfectness in selected subgames. Due to the externalities, the profitability of deviations depends on the partition formed by the remaining players: the stability of core payoff configurations is ensured by a combination of the pessimism of players going for certain profits only and the assumption that players base their stationary strategies on a made-up history punishing some of the possible deviators—and getting this sometimes right

Stationary quasi-perfect equilibrium partitions constitute the recursive core

We present sucient conditions for the implementation of the (pessimistic) recursive core (Kóczy, 2007) in discrete partition function form games using a modified version of the sequential coalition formation game by Bloch (1996) extending the results of Kóczy (2008) and - in a slightly different setup - Huang and Sjöström (2006) to games with empty residual cores (respectively, to games that are not r-balanced).Economics (Jel: A)

Stationary consistent equilibrium coalition structures constitute the recursive core

We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, GEB, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored.partition function, externalities, implementation, recursive core, stationary perfect equilibrium, time consistent equi- librium

Uniform Value in Recursive Games

We address the problem of existence of the uniform value in recursive games. We give two existence results. (i) The uniform value is shown to exist if the state space is countable, the action sets are finite and if, for some a > 0, there are finitely many states in which the limsup value is less than a. (ii) For games with non-negative payoff function, it is sufficient that the action set of player 2 is finite. The finiteness assumption can be further weakened.