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Optional games on cycles and complete graphs. (English) Zbl 1412.91007
Summary: We study stochastic evolution of optional games on simple graphs. There are two strategies, \(A\) and \(B\), whose interaction is described by a general payoff matrix. In addition, there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure.

MSC:
91A22 Evolutionary games
91A70 Spaces of games
91A43 Games involving graphs
05C57 Games on graphs (graph-theoretic aspects)
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