Learning in unprofitable games

Abstract

A game is unprofitable if equilibrium payoffs do not exceed the maximin payoff for each player. In an unprofitable game, Nash equilibrium play has been notoriously difficult to justify. For a class of $3\times 3$ games we analyze whether evolutionary and learning processes lead to Nash play. We find that neither the pure Nash equilibrium nor the pure maximin strategy are stable rest points under the studied dynamics whereas the mixed Nash equilibrium and the quantal response equilibrium may be attractors, repellors or surrounded by periodic orbits.