The Finite Horizon War of Attrition

The classical War of Attrition (Bishop and Cannings, 1978) is a pairwise conflict in which the individual willing to compete longer wins. Participation incurs a cost increasing with the length of the contest. We consider a population playing successive contests within a fixed time. An individual picks an integer length of time which is used throughout the whole time. The individuals pair at random at time zero, and at each integer time those individuals whose contests end immediately are repaired to fight a new contest. Partial results on the nature of the evolutionary stable strategy are given together with numerical studies.