Naive and sophisticated mixing: Experimental evidence

We identify a behavioral bias in some 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. We design an experiment to test for the presence of such ‘naive’ players. Our model fits the data better than the Nash equilibrium, based on simpler behavioral assumptions than those that rely on random payoff differences. In a first session, we sort subjects into naive players and their sophisticated counterparts. Two weeks later, each group played against varying proportions of automated players (bots) that follow varying off-equilibrium mixed strategies. Subjects categorized as naive 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 they are not ‘exploitation-proof.’ We also isolate altruistic components of players’ strategies: behavior skews further from Nash when doing so increases the total surplus subjects collectively obtain. Lastly, we show that the probability of being categorized as naive is correlated with the performance on a cognitive test.