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.

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Author notes

We thank the editor, two anonymous referees, Jian Song, and audiences at the University of Arizona, the University of Cologne, the University of Lyon, the University of Manchester University, Middlesex University, New York University, MPI Bonn, NHH Bergen, University of Oxford, UC San Diego, Utrecht University, University of Vienna, WZB Berlin and at IMEBESS Florence, M-BEES, NAG Toulouse, and TIBER for helpful suggestions and comments. Financial support from the Research Priority Area Behavioral Economics of the U. of Amsterdam, ANR–Labex IAST (Institute for Advanced Study in Toulouse), and Center (Tilburg U.) is gratefully acknowledged.

A supplemental appendix is available online at https://doi.org/10.1162/rest_a_00961.

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