Abstract 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.

Evolutionary explanations of anger as a commitment device hinge on two key assumptions. The first is that it is predictable, ex ante, whether someone will get angry when feeling that he or she has been badly treated. The second is that anger is associated with destructive behavior. We test the validity of these two assumptions. We collected photos of responders in an ultimatum game before they were informed about the game that they would be playing, and we filmed responders with webcams during play. We then showed pairs of photos consisting of one responder who rejected and one responder who accepted (a low offer) to an independent group of observers. We find that observers are better than chance at detecting who rejected the low offer; they do 10% better than random guessing would. We also find that anger at receiving a low offer is associated with rejection. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2017.2727 . This paper was accepted by Uri Gneezy, behavioral economics.