Models of bounded rationality and mixed equlibria: Theoretical and experimental evidence

We postulate, and then experimentally identify, a new behavioral bias in games with purely mixed equilibria. We propose the existence of naïve players who lack strategic depth; in a sense, they are the simplest possible agents that do not directly contradict the economic principle of utility maximization. When indifferent between optimal choices, they follow a simple rule-of-thumb and assign an equal probability to each. Under random matching, equilibrium is restored and is indistinguishable from Nash equilibria, as long as the percentage of naïve mixers is small enough. As such, players are unable to take advantage of their presence, and they do no worse than more sophisticated players.

We then design a two-stage experiment with non-trivial computer bots to test for the existence of naïve players. In an initial session, we sort participants into naïve players and their sophisticated counterparts. Two weeks later, each group plays against varying proportions of automated players that follow varying off-equilibrium mixed strategies. We find evidence of the existence of players that are relatively naïve and of the reaction by sophisticated players. 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, the analysis suggests that the probability of being naïve can be partially predicted by a quantitative test. 

Keywords and terms: Experimental, Behavioral, Bounded Rationality, Compensated Equilibrium, Computer Bots, Heuristics, Mixed Equilibria, Modeling Cognitive Heterogeneity, Nonlinear Diff-in-Diff, Naïve and Sophisticated Players, Two-Stage Experiment.

JEL: C72, C91, D03, D83