When two players compete for a prize, they sometimes try to act as quickly as possible. At other times, they wait and see if the other person chooses to flee first. We study this interaction in the context of a dynamic fight-or-flight game. At each moment, a player can decide to wait, flee or fight. Players are privately informed about their strengths, which in case of a battle determine who wins the prize. In the case that one player flees and manages to escape, the other player earns the prize plus a “chase-away value”. We show that the chase-away value determines if fights occur immediately or only after a waiting period. In cases where the chase-away value is positive but not too large, players can use time to learn something about the type of the opponent, as the weaker players may find it advantageous to flee earlier in the game. Weaker players thereby avoid the risk of ending up in a fight. We derive conditions under which this is the case, and test this experimentally in the lab. Our findings support the idea that endogenous timing can reduce the likelihood of a fight compared to a static version of the game (where players decide simultaneously whether to fight or flee). We also observe many fights early on in the game, even if strong players would benefit from waiting.