Two birds of the same species compete for a territory whose value in terms of evolutionary fitness is V. Each bird can adopt a hawkish or dovelike strategy in a simultaneous-move game. If both behave like doves, they split the territory. If one behaves like a dove and the other like a hawk, the hawk gets the territory. If both behave like hawks, there is a fight. The evolutionary fitness of a bird that has to fight is W. Assume that each bird is equally likely to win the fight and hence gain the territory. However, the fight is costly because of the risk of injury. We will use the model W = ½V – C, where C represents the cost of fighting. What should the birds do? Analyze the game (draw the extensive and strategic forms; identify the Nash equilibria and indicate those that are subgame-perfect equilibria) in each of the three situations below: (a) The moderate option: C < ½V. (b) The critical option: C = ½V. (c) The nuclear option: C >½V.
