Mehmet Barlo

Repeated Games with One-Memory

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an [epsilon]-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.

Bounded memory folk theorem

We show that the Folk Theorem holds for n-player discounted repeated games with bounded-memory pure strategies. Our result requires each player’s payoff to be strictly above the pure minmax payoff but requires neither time-dependent strategies, nor public randomization, nor communication. The type of strategies we employ to establish our result turn out to have new features that may be important in understanding repeated interactions.

The Optimality of Team Contracts

This paper analyzes optimal contracts in a linear hidden-action model with normally distributed returns possessing two moments that are governed jointly by two agents who have negative exponential utilities. They can observe and verify each others’ effort levels and draft enforceable side-contracts on effort levels and realized returns. Standard constraints, resulting in incentive contracts, fail to ensure implementability, and we examine centralized collusion-proof contracts and decentralized team contracts, as well. We prove that the principal may restrict attention to team contracts whenever returns from the project satisfy a mild monotonicity condition.

Stochastic Discounting in Repeated Games: Awaiting the Almost Inevitable

We study repeated games with pure strategies and stochastic discounting under perfect information, with the requirement that the stage game has at least one pure Nash action proflle. Players discount future payofis with a common, but stochastic, discount factor where associated stochastic discounting processes are required to satisfy Markov property, martingale property, having bounded increments, and possessing state spaces with rich ergodic subsets. We, additionally, demand that there are states resulting in discount factors arbitrarily close to 0, and that they are reachable with positive (yet, possibly arbitrarily small) probability in the long run. In this setting, we prove both the perfect Folk Theorem and our main result: The occurrence of any flnite number of consecutive repetitions of the period Nash action proflle, must almost surely happen within a flnite time window no matter which subgame perfect equilibrium strategy is considered and no matter how high the initial discount factor is.

Tenacious Selection of Nash Equilibrium

Abstract We propose a complexity measure and an associated refinement based on the observation that best responses with more variations call for more precise anticipation. The variations around strategy profiles are measured by considering the cardinalities of players’ pure strategy best responses when others’ behavior is perturbed. After showing that the resulting selection method displays desirable properties, it is employed to deliver a refinement: the tenacious selection of Nash equilibrium. We prove that it exists; does not have containment relations with perfection, properness, persistence and other refinements; and possesses some desirable features.