TY - JOUR
T1 - Stochastic evolutionary dynamics of direct reciprocity
JF - Proceedings of the Royal Society B: Biological Sciences
JO - Proc Biol Sci
SP - 463
LP - 468
M3 - 10.1098/rspb.2009.1171
VL - 277
IS - 1680
AU - Imhof, Lorens A.
AU - Nowak, Martin A.
Y1 - 2010/02/07
UR - http://rspb.royalsocietypublishing.org/content/277/1680/463.abstract
N2 - 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 ‘knock-out experiments’ to study how various strategies affect the evolution of cooperation. We find that ‘tit-for-tat’ is a weak catalyst for the emergence of cooperation, while ‘always cooperate’ 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. © 2009 The Royal Society
ER -