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 variance of random disturbances. 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 investigate the limiting QRE in normal form games, and analyze the effects of payoff transformations and adding/eliminating dominated strategies on equilibrium selection. We find that in two-person symmetric games, any strict Nash equilibrium can be selected as the limiting QRE by appropriately adding a single strictly dominated strategy.