Article,
Stochastic evolutionary dynamics of direct reciprocity
Proceedings of the Royal Society B: Biological Sciences, 277 (1680): 463--468 (Feb 7, 2010)
DOI: 10.1098/rspb.2009.1171
Abstract
Evolutionary game theory is the study of frequency-dependent selection. The success of an individual depends on the frequencies of strategies that are used in the population. We propose a new model for studying evolutionary dynamics in games with a continuous strategy space. The population size is finite. All members of the population use the same strategy. A mutant strategy is chosen from some distribution over the strategy space. The fixation probability of the mutant strategy in the resident population is calculated. The new mutant takes over the population with this probability. In this case, the mutant becomes the new resident. Otherwise, the existing resident remains. Then, another mutant is generated. These dynamics lead to a stationary distribution over the entire strategy space. Our new approach generalizes classical adaptive dynamics in three ways: (i) the population size is finite; (ii) mutants can be drawn non-locally and (iii) the dynamics are stochastic. We explore reactive strategies in the repeated Prisoner's Dilemma. We perform âknock-out experimentsâ to study how various strategies affect the evolution of cooperation. We find that âtit-for-tatâ is a weak catalyst for the emergence of cooperation, while âalways cooperateâ is a strong catalyst for the emergence of defection. Our analysis leads to a new understanding of the optimal level of forgiveness that is needed for the evolution of cooperation under direct reciprocity.
