A Quantal Response Equilibrium Model of Order Statistic Games

This paper applies quantal response equilibrium (QRE) models (McKelvey and Palfrey, Games and Economic Behavior 10 (1995), 6-38) to a wide class of symmetric coordination games in which each player's best response is determined by an order statistic of all players' decisions, as in the classic experiments of Van Huyck, Battalio, and Beil (American Economic Review 80 (1990), 234-248; Quarterly Journal of Economics 106 (1991), 885-910), but players have a bounded continuum of decisions, which approximates to Van Huyck, Battalio, and Rankin's (1996) environment. Generalizing the results of Anderson, Goeree, and Holt (1998) with a quadratic payoff function, I show that as the noise vanishes the QRE approaches the most efficient equilibrium as a unique limit for all order statistics, including the minimum.