# Stochastic Strategy Adjustment in Coordination Games

Kosfeld, M (2002). Stochastic Strategy Adjustment in Coordination Games. Economic Theory, 20(2):321-339.

## Abstract

The paper explores a model of equilibrium selection in coordination games, where agents from an infinite population stochastically adjust their strategies to changes in their local environment. Instead of playing perturbed best-response, it is assumed that agents follow a rule of switching to better strategies with higher probability'. This behavioral rule is related to bounded-rationality models of Rosenthal (1989) and Schlag (1998). Moreover, agents stay with their strategy in case they successfully coordinate with their local neighbors. Our main results show that both strict Nash equilibria of the coordination game correspond to invariant distributions of the process, hence evolution of play is not ergodic but instead depends on initial conditions. However, coordination on the risk-dominant equilibrium occurs with probability one whenever the initial fraction contains infinitely many agents, independent of the spatial distribution of these agents.

The paper explores a model of equilibrium selection in coordination games, where agents from an infinite population stochastically adjust their strategies to changes in their local environment. Instead of playing perturbed best-response, it is assumed that agents follow a rule of switching to better strategies with higher probability'. This behavioral rule is related to bounded-rationality models of Rosenthal (1989) and Schlag (1998). Moreover, agents stay with their strategy in case they successfully coordinate with their local neighbors. Our main results show that both strict Nash equilibria of the coordination game correspond to invariant distributions of the process, hence evolution of play is not ergodic but instead depends on initial conditions. However, coordination on the risk-dominant equilibrium occurs with probability one whenever the initial fraction contains infinitely many agents, independent of the spatial distribution of these agents.

## Citations

10 citations in Web of Science®
11 citations in Scopus®

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Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Economics 330 Economics Equilibrium selection, Coordination game, Evolution, Strategy adjustment English September 2002 11 Feb 2008 12:29 05 Apr 2016 12:22 Springer 0938-2259 The original publication is available at www.springerlink.com 10.1007/s001990100223
Permanent URL: http://doi.org/10.5167/uzh-2223