Reputation without commitment in finitely-repeated games

Games and Economic Behavior, 1997

We consider a wide class of repeated common interest games perturbed with one-sided incomplete information: one player (the informed player) might be a commitment type playing the Pareto dominant action. As discounting, which is assumed to be symmetric, and the prior probability of the commitment type go to zero, it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium.

Journal of Economic Theory, 1996

We analyze reputation in a game between a large player and a continuum of long-lived small players in which state variables affect players' payoffs. The large player's type is private information. We give conditions under which in every Nash equilibrium a very patient large player will get almost the largest payoff consistent with the small players choosing a best response in a large finite truncation of the game. While our results apply to the time inconsistency problem of optimal government policy, we show that for the durable goods monopoly reputation may fail to improve the monopolist's payoff. Journal of Economic Literature Classification Numbers: C72, C73.

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.

Mathematics of Operations Research, 1986

We consider N person repeated games with complete information and standard signalling. We first prove several properties of the sets of feasible payoffs and Nash equilibrium payoffs for the n-stage game and for the λ-discounted game. In the second part we determine the set of equilibrium payoffs for the Prisoner's Dilemma corresponding to the critical value of the discount factor.

2007

This paper studies reputation effects in a 2&player repeated moral hazard game. A long&lived player, Player 1, would benefit if he could commit to playing a particular action which is strictly dominated in the stage game. His opponent, who may be either long& ...

Handbook of game theory with economic applications, 1992

We consider N person repeated games with complete information and standard signalling. We first prove several ptopeities of the sets of feasible payo^s and Nash equilibrium payoffs for the n-stage game and for the X-discounted game. In the second part we determine the set of equilibrium payoffs for the Prisoner's Dilemma corresponding to the critical value of the discount factor. 0. IntrodiK^ioii. We consider iV-person repeated games with complete information and standard signalling. We introduce the n-stage game, the X-discounted game and the infinitely repeated game; then we prove several properties conceming the sets of feasible payoffs and of Nash equilibrium payoffs. The properties studied are mainly the relation between convexity and stationarity and the simply-connectedness of the set of feasible payoffs. The second part of the paper is devoted to^the study of the X-discounted Prisoner's Dilemma. If X is greater than a critical value X the only Nash equilibrium payoff is the usual one (like in any finite repetition). Then we determine exactly the set of Nash equilibrium in the game with tibiis discount factor X, and this is a connected set of dimension 2 which differs from the set of individually rational feasible payoffs.

2015

This paper characterizes equilibrium outcomes of extensive form games with incomplete in-formation in which players sign renegotiable contracts with third parties. Our aim is to under-stand the extent to which third-party contracts can be used as commitment devices when it is im-possible to commit not to renegotiate them. We characterize renegotiation-proof contracts and strategies for extensive form games with incomplete information and apply our results to two-stage games. If contracts are observable, then the second mover obtains the best possible payoff given that she plays an incentive compatible and renegotiation-proof strategy and the first mover best responds. If contracts are unobservable, then any Bayesian Nash equilibrium outcome of the original game in which the second mover plays an incentive compatible and renegotiation-proof strategy can be supported. We apply our results to Stackelberg competition and show that renegotiation-proofness imposes a very simple restrictio...

1992

The "chain-store paradox" of Reinhard Sehen is one of a number of scenarios involving the finite repetition of a certain kind of sub-game about which a paradoxical conclusion can be derived. In each of these cases, a backward-induction argument is used to prove that it is futile to try to establish a reputation for cooperative or punitive behavior through appropriate action in the early stages of the game, despite the fact that nearly all agree that it is intuitively reasonable to do so. Selten believed that this is paradoxical in the weak sense: a surprising, unexpected result of game theory. In this paper, I argue that it is paradoxical in the strong sense: a logical antinomy of rational belief or subjective probability, analogous to the paradox of the Liar.

OF THE DISSERTATION ESSAYS ON REPUTATION by Marco Celentani Doctor of Philosophy in Economics University of California, Los Angeles, 1993 Professor David K. Levine, Chair The goal of the literature on reputation eects is to provide equilibrium characterizations for games in which there is some uncertainty relative to the utility function of a player. The purpose of this dissertation is to study the conditions under which this kind of reputational argument can be applied to frameworks that are interesting for their economic applications. Chapter 2 considers a repeated game between a long run player and a sequence of short run players who are alive for one period only and therefore do not care about the future. When the stage game is allowed to be a sequential move one, if a short run player does not expect the long run player to play in a certain way, he might choose an action that does not reveal the strategy chosen by the long run player. Chapter 2 introduces a perturbation on the ...

1997

We investigate a game in which there is a long-run player who has private information about how long will the game last, who must precommit to an action, and who faces a sequence of short-run players who get a noisy signal of that action. We might expect such a long-lived long-run player to behave as a Stackelberg leader since most short-run players will eventually learn the true action. However, short-run players know that a long-run player that has been in the game for a long time must have chosen the Stackelberg action and may ignore the evidence from the signal. If so, the long-run player may have no reason to actually choose the Stackelberg action. We show that if there is a chance that the long-run player chooses other action by mistake, and the signal is sufficiently informative, this paradox can be resolved.