Solution
Hawk-Dove
Show the problem again
Two animals contest a resource worth V = 2. Hawks fight: against a Dove they take everything, but two Hawks fight at cost C = 4, for expected payoff (V − C)/2 each. Doves split the resource peacefully and flee from Hawks. In the evolutionarily stable strategy, with what probability is Hawk played? Express as a fraction.
Worked solution
The answer is V/C = 1/2. Neither pure strategy is stable: Hawks invade Doves (2 vs 1) and Doves invade Hawks (0 vs −1). The mixed ESS makes both actions equally fit: with Hawk frequency p, Hawk earns p(−1) + (1−p)(2) and Dove earns p(0) + (1−p)(1); equating gives p = 1/2 = V/C. Costly fights persist in equilibrium exactly often enough to deter total aggression.
Source: Introduced by John Maynard Smith and George Price, 'The Logic of Animal Conflict' (1973). Statement written for AxiomIQ.