An Application of Decision Theoretical Models of Probabilistic Choice to Solving 2x2 Simultaneous-Move Noncooperative Games in the Normal Form

Abstract

Several models of probabilistic choice under uncertainty allow for deterministic choice if one act state-wise dominates the other. Such models have a natural application in game theory where probabilistic choice corresponds to mixed strategies, deterministic choice — to pure strategies and state-wise dominance — to strategic dominance. This paper considers an application to the simplest possible 2x2 simultaneous-move noncooperative game in the normal form. We derive a new equilibrium solution concept that coincides with the standard Nash equilibrium in pure strategies but resembles a quantal response equilibrium in mixed strategies. In particular, players randomize between strategies not in order to keep their opponent indifferent between his or her strategies (as in the mixed strategy Nash equilibrium) but because they are more likely to (but not always) choose strategies yielding higher utility.