Practical Performance of Refinements of Nash Equilibria in Extensive-Form Zero-Sum Games

Nash equilibrium (NE) is the best known solution concept used in game theory. It is known that NE is particularly weak even in zero-sum extensive-form games since it can prescribe irrational actions to play that do not exploit mistakes made by an imperfect opponent. These issues are addressed by a number of refinements of NE that strengthen the requirements for equilibrium strategies. However, a thorough experimental analysis of practical performance of the Nash equilibria refinement strategies is, to the best of our knowledge, missing. This paper aims to fill this void and provides the first broader experimental comparison of the quality of refined Nash strategies in zero-sum extensive-form games. The experimental results suggest that (1) there is a significant difference between the best and the worst NE strategy against imperfect opponents, (2) the existing refinements outperform the worst NE strategy, (3) they typically perform close to the best possible NE strategy, and (4) the difference in performance of all compared refinements is very small.