A Correction and Re-Examination of 'Stationary Concepts for Experimental 2 x 2 Games'

Abstract

Selten and Chmura (American Economic Review, June 2008, 98(3), 938-966) recently reported experimental laboratory results for 2 x 2 games with unique mixed-strategy equilibria used to compare Nash equilibrium with four other stationary concepts: quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium, and impulse balance equilibrium. They conclude that impulse balance equilibrium performs best, and, in particular, significantly outperforms quantal response equilibrium. We reanalyze their data and correct some errors. The reanalysis shows that Nash clearly fits worst but the four other concepts perform about equally well. It is surprising that four models, which are so conceptually different, are so close in accuracy, and following Selten and Chmura's suggestion, we report new analysis of previous experiments on 2 x 2 games with unique mixed-strategy equilibria. These additional tests show the importance of the loss aversion that is hardwired into impulse balance equilibrium: when the other non-Nash stationary concepts are augmented with loss aversion they outperform impulse balance equilibrium.