Naive and Sophisticated Mixing: Experimental Evidence

We identify a behavioral bias in games with completely mixed equilibria. Following Alcocer and Jeitschko (2014) we characterize players who, when indifferent between several optimal choices, assign an equal probability to playing any one of them, rather than following the mixing of the Nash Equilibirum. We design an experiment to test for the presence of such ‘na ̈ıve’ players. In a first session, we sort subjects into na ̈ıve players and their sophisticated counterparts, according to their tendency to skew towards uniform mixing rather than Nash equilibrium mixing. Two weeks later, each group played against varying proportions of automated players (bots) that follow varying off-equilibrium mixed strategies. Subjects categorized as na ̈ıve continue to tend towards uniform mixing and also are less apt to account for distortions due to off-equilibrium bots. In contrast, sophisticated players do compensate for the distortions in the game, although this compensation is not large enough to restore equilibria, implying there are predictable methods to attain above-equilibrium payoffs. We also isolate altruistic components of players’ strategies: behavior gets closer to Nash equilibria by adding transparent bots that do not directly incentivize any change in behavior but decrease the benefits of surplus maximizing behavior. Lastly, we show that the probability of being categorized as na ̈ıve is correlated with the performance on a quantitative test.