Epstein Secrets

f its transitions and the ease with which the survival game may be embedded within it, we base our model on the haploid population-genetic model of Moran (1958).The standard version of the Moran model pairs single births and deaths such that the population size remains constant. In the absence of se

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

t much larger than the degree, as well as the phenotype space. 2.5.1 The well-mixed population As first example we consider the frequency dependent Moran process in a well mixed population of size N (Nowak et al 2004, Taylor et al 2004, Nowak 2006a) (Fig.la). In the language of evolutionary graph the

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

weak selection (as opposed to 6 cc 1) shall become clear at the end of this section. The dynamics of the system is given by the frequency dependent Moran process. In each time step a randomly chosen individual is replaced by a copy of an individual chosen with probability proportional to its payoff.

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