Independent mistakes in large games

Abstract

Economic models usually assume that agents play precise best responses to others' actions.It is sometimes argued that this is a good approximation when there are many agents in the game, because if their mistakes are independent, aggregate uncertainty is small. We study a class of games in which players' payoffs depend solely on their individual actions, and on the aggregate of all players' actions. We investigate whether their equilibria are affected by mistakes when the number of players becomes large. Indeed, in generic games with continuous payoff functions, independent mistakes wash out in the limit. This may not be the case if payoffs are discontinuous.As a counter-example we present the n players Nash bargaining game, as well as a large class of "free-rider games." * I am grateful for the helpful comments of Elchanan Ben-Porath, Varadarajan

Behaviorally Optimal Auction Design: Examples and Observations

“…6 Costa-Gomes and Crawford (2006) and Costa-Gomes et al (2009) summarize the evidence in support of level-k models and present the case for using them to model initial responses to games. Until recently the choices for modeling nonequilibrium behavior were limited to rationalizability; adding noise to equilibrium predictions as in Pauzner (2000); or using McKelvey and Palfrey's (1995) notion of quantal response equilibrium ("QRE"). To our knowledge these models have not been applied to design, perhaps because rationalizability is imprecise (but see Battigalli and Siniscalchi 2003); QRE must be solved numerically; and in noisy equilibrium or QRE the error specification is crucial but has little to guide it (Costa-Gomes, Crawford, and Iriberri 2009).…”