Characterising equilibrium selection in global games with strategic complementarities (original) (raw)

Economics 703: Microeconomics II Modelling Strategic Behavior1

2011

Remark 1.1. 1 The definition per se of a normal form game (or strict dominance for that matter) makes no assumption about the knowledge that players have about the game. We will, however, typically assume (at least) that players know the strategy spaces, and their own payoffs as a function of strategy profiles. However, as the large literature on evolutionary game theory in biology suggests (see also Section 4.2), this is not necessary.

Repeated Games With Intervention: Theory and Applications in Communications

2011

In communication systems where users share common resources, users' selfish behavior usually results in suboptimal resource utilization. There have been extensive works that model communication systems with selfish users as one-shot games and propose incentive schemes to achieve Pareto optimal action profiles as non-cooperative equilibria. However, in many communication systems, due to strong negative externalities among users, the sets of feasible payoffs in one-shot games are nonconvex. Thus, it is possible to expand the set of feasible payoffs by having users choose convex combinations of different payoffs. In this paper, we propose a repeated game model generalized by intervention. First, we use repeated games to convexify the set of feasible payoffs in one-shot games. Second, we combine conventional repeated games with intervention, originally proposed for one-shot games, to achieve a larger set of equilibrium payoffs and loosen requirements for users' patience to achieve it. We study the problem of maximizing a welfare function defined on users' equilibrium payoffs, subject to minimum payoff guarantees. Given the optimal equilibrium payoff, we derive the minimum intervention capability required and design corresponding equilibrium strategies. The proposed generalized repeated game model applies to various communication systems, such as power control and flow control.

Reputation in the long-run with imperfect monitoring

2011

We study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stage-game actions of player two imperfectly, while player two monitors the pure stage-game actions of player one perfectly. Player one's type is private information and he may be a “commitment type,” drawn from a countable set of commitment types, who is locked into playing a particular strategy.

Reputation with Long Run Players

2008

Abstract. Previous work shows that reputation results may fail in repeated games with long-run players with equal discount factors. Attention is restricted to extensive-form stage games of perfect information. One and two-sided reputation results are provided for repeated games with two long-run players with equal discount factors where the first mover advantage is maximal.

Reputation with long run players and imperfect observation

2008

Zusammenfassung: Previous work shows that reputation results may fail in repeated games between two long-run players with equal discount factors. We restrict attention to an infinitely repeated game where two players with equal discount factors play a simultaneous move stage game where actions of player 2 are imperfectly observed. The set of commitment types for player 1 is taken as any (countable) set of finite automata. In this context, for a restricted class of stage games, we provide a one sided reputation result.

Reputation in Long-Run Relationships

2011

Abstract We model a long-run relationship as an infinitely repeated game played by two equally patient agents. In each period, the agents play an extensive-form stage game of perfect information with either locally non-conflicting interests or strictly conflicting interests. There is incomplete information about the type of Player 1, while Player 2's type is commonly known.

Aggregate Representations of Aggregate Games

2011

An aggregate game is a normal-form game with the property that each player's payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characterizations of equilibrium aggregates without first requiring that one solves for the equilibrium strategy profile. We demonstrate that the defining nature of payoffs in an aggregate game allows one to embed the strategic analysis into the aggregate-strategy space, converting an n-player game to a simpler object -a self-generating single-person maximization program. We apply these techniques to a number of economic settings including competition in supply functions or competitive agency games with nonlinear transfer functions.

Imperfect monitoring and impermanent reputations

Econometrica, 2004

We study the long-run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not eventually play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for non-credible behavior in the presence of imperfect monitoring.