War of attrition (game)

In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. The model was originally formulated by John Maynard Smith (1974). Strategically, the game is an auction, in which the prize goes to the player with the highest bid, and both players pay the loser's low bid.

The evolutionarily stable strategy when playing this game is a probability density of random persistence times which cannot be predicted by the opponent in any particular contest. This result has led to the prediction that threat displays ought not to evolve.