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 between 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.