Epstein Secrets

haviors or strategies. When both players are present. each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to Zero. We obtain general, analytical results for n-st

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

ase the problem can be reduced to computing absorption probabilities in Marken, chains, where each state represent the number of mutants. Hence the Markov chain Ls linear in the number of vertices of the graphs, and since absorption probabilities in Markov chains can be computed in polynomial time (by

ualitative I. Nowak MA. May RM (1992) Emlutionay gams and mad chaos. Nature BOA 2. Killingback T. Ociegia M (1996) Spatial evolutionary game showy: Hawks and doves malted. Prot. FL Soc. B 2634137421135-1144. 3. Seat., G. Take C (1996) Evolutionary Mantis ek.na Vine on a mime laths Phys. Rev. E. 56(1

given time [35]. Then we can use the fixation probabilities, or their large N asymptotic values [5, 155], and describe the system effectively as a Markov process on n homogeneous strategy states. This description, however, can lead to very different conditions for arbitrary selection and for weak sele

. 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