SCORE-DEPENDENT FERTILITY MODEL FOR THE EVOLUTION OF COOPERATION IN ALATTICE

The evolution of cooperation is studied in a lattice-structured popula tion, in which each individual plays the iterated Prisoner's Dilemma g ame with its neighbors. The population includes Tit-for-Tat (TFT, a co operative strategy) and All Defect (AD, a selfish strategy) distribute d over the lattice points. An individual dies randomly, and the vacant site is filled immediately by a copy of one of the neighbors in which the probability of colonization success by a particular neighbor is p roportional to its score accumulated in the game. This ''score-depende nt fertility model'' (or fertility model)behaves very differently from score-dependent viability model (viability model) studied in a previo us paper. The model on a one-dimensional lattice is analysed by invasi on probability analysis, pair-edge method mean-held approximation, pai r approximation, and computer simulation. Results are: (1) TFT players come to form tight clusters. When the probability of iteration w is l arge, initially rare TFT can invade and spread in a population, domina ted by AD, unlike in the complete mixing model. The condition for the increase of TFT is accurately predicted by all the techniques except m ean-field approximation; (2) fertility model is much more favorable fo r the spread of TFT than the corresponding viability model, because sp iteful killing of neighbors is favored in the viability model but not in the fertility model; (3) eight lattice games on two-dimensional lat tice with different assumptions are examined. Cooperation and defects can coexist stable in the models of deterministic state change but not in the models of stochastic state change. (C) 1998 Academic Press.