Inference For Nash Equilibrium Profiles In A Simultaneous Discrete Game

This paper studies a simultaneous,complete-information game played by N players with ordered actions.I extend the static model of quantity competition in Davis(2006)to heterogeneous case and allows for heterogeneous competitive effect.Players’strategic effects are reflected by an index function named weighted market index,which is the linear combinations of their strategies.I prove the existence of pure strategy Nash equilibrium and show that profiles’ difference in weighted market index will be less than the maximal weight if they are Nash equilibria in the same game.Based on these implications,I construct the confidence set whose probability of covering the market outcome is no less than(1-α)%for any valid selection mechanism and give the feasible estimators.Similar to Aradillas-Lopez(2011),I characterize bounds for the probability that a given profile is Nash equilibrium and deduce a lower bound for the probability that the selection mechanism chooses it.Based on local constant method,we give nonparametric estimators for the confidence set and these probabilities and discuss their asymptotic properties.The empirical illustration is a multiple entry game in the U.S.drugstore industry.