On the Uniqueness of Quantal Response Equilibria

This paper establishes the uniqueness of a Quantal Response Equilibrium (QRE) for a broad class of $n$-person normal form games. We show that the uniqueness of a QRE is determined by a precise relationship between a measure of players' payoff concavity, a bound on the intensity of strategic interaction, and the number of players in the game. Our results do not require specific parametric assumptions on players' payoffs nor in the distribution of preference shocks. As an application we study the uniqueness of a QRE in the case of large network games. For this class of games, we show how the interaction between the network topology and the impact of players' unilateral deviations determines the uniqueness of a QRE