On the Uniqueness of Quantal Response Equilibria and Its Application to Network Games
48 Pages Posted: 2 Jul 2020 Last revised: 11 Nov 2021
Date Written: June 29, 2021
This paper studies the uniqueness of a Quantal Response Equilibrium (QRE) in a broad class of $n$-person normal form games. We make three main contributions. First, we show that the uniqueness of a QRE is determined by a precise relationship between the strong concavity of players' payoffs, a bound on the intensity of strategic interaction, and the number of players in the game. Second, we introduce three new parametric models which allow for correlation among alternatives: the Generalized Nested Logit (GNL), the Ordered Generalized Extreme Value (OGEV), and the Nested Logit (NL) models. For these three models, we provide a simple uniqueness condition which captures the degree of correlation between players' actions. Finally, we apply our results to the study of network games. In particular, we apply the OGEV model to study treatment participation and public goods games. In addition, we apply the NL model to study technology adoption in networked environments. In these three applications, we show that the uniqueness of a QRE is determined by the network topology and its interaction with a measure of correlation between players' actions.
Keywords: QRE, Discrete choice, Logit-QRE, Network games, Variational Inequalities
JEL Classification: C72, D85, H41
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