Emergence of Cooperation with chain-reaction-extinction

Last modified: 2014-03-28

#### Abstract

We study a chain-reaction-extinction model on simple graph. Interaction between species is mimicked by a prisoner’s dilemma gamewith a memoryless stochastic strategy and the fitness of a species isgiven by the payoffs of games with its neighbors.We investigate the evolution dynamics with Monte Carlo methodwith two-types of extinction processes, fitness dependent extinctionand chain-reaction-extinction. In the former, the extinction probability of aspecies with fitness f is proportional to exp(-f/T) with‘temperature’ T. The neighbors of the extinct species are alsoextinct with a probability W. When a cooperatorinteracts with defectors, the cooperator is likely to be extinct dueto its low payoff, but the neighboring defectors also tend todisappear through chain-reaction-extinction, giving rise to anassortment of cooperators. Owing to this assortment, cooperation canemerge for a wider range of W values than the mean-field prediction. In the zero-temperature limit, cooperation evolves at any finite W.