Quantal Response Methods for Equilibrium Selection in Normal Form Games

Abstract

This paper describes a general framework for equilibrium selection by tracing the graph of the quantal response equilibrium (QRE) correspondence as a function of the estimation error. If a quantal response function satisfies C2 continuity, monotonicity and cumulativity, the graph of QRE correspondence generically includes a unique branch that starts at the centroid of the strategy simplex and converges to a unique Nash equilibrium as noises vanish. This equilibrium is called the limiting QRE of the game. We then provide sufficient conditions for the limiting QRE in normal form games, J×J symmetric games and J×J bimatrix games. Based on these conditions, the effects of payoff transformations and adding/eliminating dominated strategies on equilibrium selection are investigated. We find that in J×J symmetric games, any strict Nash equilibrium can be selected as the limiting QRE by appropriately adding a single strictly dominated strategy.

Keywords: Quantal response equilibrium; equilibrium selection; normal form game; symmetric game; dominated strategy

JEL Classification: C62; C73; D50