A Refinement of Logit Quantal Response Equillibrium

Abstract

Unlike the Nash equilibrium, logit quantal response equilibrium is affected by positive affine transformations of players’ von Neumann-Morgenstern utility payoffs. This paper presents a modification of a logit quantal response equilibrium that makes this equilibrium solution concept invariant to arbitrary normalization of utility payoffs. Our proposed modification can be viewed as a refinement of a logit quantal response equilibria: instead of obtaining a continuum of equilibria (for different positive affine transformations of utility function) we now obtain only one equilibrium for all possible positive affine transformations of utility function. We define our refinement for simultaneous-move noncooperative games in the normal form. An interpretation of our refinement in terms of the implicit model of relative random errors is provided.

Keywords: Equilibrium Solution Concept, Nash Equilibrium, Quantal Response Equilibrium, Simultaneous-Move Noncooperative Game, Normal Form

JEL Classification: C72, D81