Fast Equilibrium Selection by Rational Players Living in a Changing World

Abstract

We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk-dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2 = 2 game. The payoff matrix changes according to a random walk. Players observe these payoffs and the population distribution of actions as they evolve. The game has frictions: opportunities to change strategies arrive from independent random processes, so that the players are locked into their actions for some time. As the frictions disappear, each player ignores what the others are doing and switches at her first opportunity to the risk-dominant action. History dependence emerges in some cases when frictions remain positive.

Equilibrium selection in global games with strategic complementarities

“…In each of these cases, we characterize the selected equilibrium. 3 Strategic complementarities are present in many settings, including macroeconomic coordination failures, technology adoption, oligopoly, R&D competition, coordination in teams, arms races, and pretrial bargaining. 4 In a number of recent applied papers, the global games approach has been used to select a unique equilibrium.…”

“…The connection between our findings and existing results on supermodular games is discussed in the conclusion. 3 In cases (1) and (2), there is own-action quasiconcavity since there are only two actions. In case (3), noise-independent selection holds even without own-action quasiconcavity.…”

Coordination, timing and common knowledge

“…Takahashi (2008) highlights the formal connection between global games and perfect foresight dynamics. Frankel and Pauzner (2000) and Burdzy, Frankel, and Pauzner (2001) study a setting where a payo¤ relevant state evolves according to a stochastic process and is publicly observed. A continuum population receive opportunities to revise their behavior according to a Poisson clock.…”

“…Guimaraes (2006) and He and Xiong (2012) consider situations where, like Frankel and Pauzner (2000) and Burdzy, Frankel, and Pauzner (2001), a payo¤ relevant state evolves according to some stochastic process and is publicly observed. In the currency attack model of Guimaraes (2006), investors observe the state of a national economy; in the debt rollover model of He and Xiong (2012), investors observe the state of a company whose debt they hold.…”

Incertitude stratégique et sélection d’équilibre : deux applications

“…Chaque maison du quartier est vendue au plus offrant, c'est-à-dire à l'agent dont la disposition à payer est la plus grande. Le modèle comporte en plus des frictions qui empêchent les agents de changer de localisation à chaque instant : un agent reçoit de manière aléatoire l'occasion de déménager (la technique générale nécessitant la présence de ces frictions est discutée dans Burdzy, Frankel et Pauzner (2001)). Ainsi, lorsqu'un agent reçoit la possibilité de déménager, il vend sa maison à l'acheteur le plus offrant (qui peut être l'agent lui-même, auquel cas il continue d'occuper sa maison).…”