Evolutionary Games On Cycles By Group Selection

In this paper, the stochastic evolutionary game on the simplest possible graph (the cycle) with group selection is studied. Three mechanisms for the evolution of cooperation (direct reci-procity, network reciprocity and group selection) are considered. Then, some exact conditions for natural selection to favour one strategy over another strategy are obtained. There are four chapters in this paper.In the first chapter, we make preliminary remarks about evolutionary game dynamics in finite populations, review and introduce some recent research on the three mechanisms for the evolution of cooperation in the Prisoner's Dilemma. For each mechanism the transformations of the Prisoner's Dilemma payoff matrix are given. Finally, the main purpose of this paper are introduced.In the second chapter, we propose a stochastic model of group selection on cycles. A population is subdivided into groups with links at different rates. And individuals in group inter-act only with their two neighbours on a cycle. The fundamental conditions for the evolution of cooperation by group selection on cycles are derived. Then, we allow for some migration of indi-viduals between groups and derive the corresponding conditions for the evolution of cooperation. All these conditions hold in the limit of weak selection and rare group splitting.In the third chapter, we study some models of evolutionary games on cycles by group selec-tion. The fundamental conditions for the evolution of cooperation are derived in the model where direct reciprocity, group selection and network reciprocity occur simultaneously. Furthermore, the effect of the simplest possible graph (the cycle) on evolutionary of cooperation is analyzed. Then, the case with non-uniform interaction rates is studied, and their effect on the evolution of cooperation is analyzed. Finally, the case of breaking the symmetry between interaction and replacement is discussed, and a condition for the evolution of cooperation is obtained.In the last chapter, we summarize this paper. We present evolutionary games on cycles by group selection and derive the fundamental conditions for the evolution of cooperation which hold in the limit of weak selection and rare group splitting.