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Free keywords:
complex systems; cooperation; evolutionary dynamics; finite structured population; public goods game; pair approximation
Abstract:
The evolution of cooperation opens a prominent window to investigate the organizing properties in complex systems.
The boom of complex networks paves the way to describe structured population and it has been introduced into evolutionary
game theory recently. Yet, for multi-player games, theoretical works so far have been only on cycle and well-mixed population.
With the metaphor of public goods game, we have considered the stochastic dynamics in finite structured population where the
average degree of the population is k. A simple rule, i.e., the benefit to cost ratio should exceed (k + 1)2=(k + 3), is obtained
analytically. This rule not only guarantees the emergence of cooperation, but also ensures the stabilization of cooperation under
weak selection. Besides, inspired by pair approximation, we find some evidence supporting the thesis of spatial reciprocity in
multiple players games to some extend. Our results may give a criteria suggesting when cooperation can be favored in finite
structured population.
