We study a dynamic game in which players compete for a prize. In a waiting game with two-sided private information about strength levels, players choose fighting, fleeing, or waiting. Players earn a “deterrence value” on top of the prize if their opponent escapes without a battle. We show that this value is a key determinant of the type of equilibrium. For intermediate values, sorting takes place, with weaker players fleeing before others fight. Time then helps to reduce battles. In an experiment, we find support for the key theoretical predictions and document suboptimal predatory fighting.

Despite decades of research on heuristics and biases, evidence on the effect of large incentives on cognitive biases is scant. We test the effect of incentives on four widely documented biases: base-rate neglect, anchoring, failure of contingent thinking, and intuitive reasoning. In laboratory experiments with 1,236 college students in Nairobi, we implement three incentive levels: no incentives, standard lab payments, and very high incentives. We find that very high stakes increase response times by 40% but improve performance only very mildly or not at all. In none of the tasks do very high stakes come close to debiasing participants.