Epstein Secrets

in which having a different behavior than one's partner produces a higher payoff. Doves cooperate by sharing resources but retreat when challenged. Hawks do not cooperate. They are ready to fight to avoid leaving an interaction empty-handed. A Hawk gets the entire resource when facing a Dove but suff

30 40 60 60 70 80 Number of Iterations, n Fag. 0. Values °IG(n) — c(n) and b(n) — d(n) over n = 1...80 iterations for two games which begin as Prisoner's Dilemmas at n = I. In both cases, the loner survival probabilities are ck, = 4 = 0.9. PanelA: a = 0.97.6 = 0.94. c = 0.99,d = 0.95; these are the

14 6.2 Mixed games with 2 strategies 119 6.3 Mixed games with two pure strategies 122 6.3.1 A resealed payoff matrix 125 6.3.2 Example: Hawks and Doves 126 6.4 A mixed 3-game: Cooperators, Defectors, Loners 130 6.5 Mixed games with n pure strategies 135 6.6 Conclusion 136 B

asier it is for cooperators to outcompete defectors. We give a simple relationship between a and the critical benefit-to-cost ratio in a simplified Prisoner's Dilemma game. (War +1 a — (NW —1. This shows that for the purpose of establishing strategy dominance, in the limit of weak selection, it suffice

. 0, the mixed phase extends to the quarter-plane a > 0, > 0. For large mutation ratesµ —• co, however, the mixed phase disappears. 6.3.2 Example: Hawks and Doves As an example, we consider the Hawk-Dove game (Maynard-Smith 1982, Houston Mcishunara 1988, Houston Sc McNamara 1991, IvIesterton-Gibbons

rs on Cooperators and Defectors. Then in 5.3.2 we show how mutation alone can make a strategy more abundant. Finally in 5.3.3 we study the repeated Prisoner's Dilemma game. 5.3.1 Cooperators, Defectors, Loners To see the difference between our weak selection and a traditional game-theoretic approach, l