Games of competition in a stochastic environment

The paper presents a set of games of competition between two or three players in which reward is jointly determined by a stochastic biased mechanism and players' choices. More specifically, a resource can be found with unequal probabilities in one of two locations. The first agent is rewarded only if it finds the resource and avoids being found by the next agent in line; the latter is rewarded only if it finds the former. Five benchmarks, based on different psychological and game-theoretic assumptions are derived and their predictions compared to actual behavior of 120, 40, and 48 participants playing repeatedly. Of the five benchmarks – the unique (Nash) equilibrium, reinforcement learning, trust-based efficiency, maximum unpredictability, and regret-based (Impulse Balance) equilibrium – regret for missed opportunities best accounts for the qualitative aspect of participants' behavior and regret attenuated by randomization best accounts for the quantitative aspect of behavior.