Naive versus Sophisticated Mixing: Experimental Evidence, with Thomas D. Jeitschko and Robert Shupp
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 Equilibrium. We design an experiment to test for the presence of such ‘naive’ players. In a first session, we sort subjects into naive 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 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 closer towards Nash when doing so does not affect the total surplus subjects collectively obtain. Lastly, we show that the probability of being categorized as naive is correlated with the performance on a quantitative test.
