Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies

Abstract

Cooperation and defection may be considered as two extreme responses to a social dilemma. Yet the reality is much less clear-cut. Between the two extremes lies an interval of ambivalent choices, which may be captured theoretically by means of continuous strategies defining the extent of the contributions of each individual player to the common pool. If strategies are chosen from the unit interval, where 0 corresponds to pure defection and 1 corresponds to the maximal contribution, the question is what is the characteristic level of individual investments to the common pool that emerges if the evolution is guided by different benefit functions. Here we consider the steepness and the threshold as two parameters defining an array of generalized benefit functions, and we show that in a structured population there exist intermediate values of both at which the collective contributions are maximal. However, as the cost-to-benefit ratio of cooperation increases the characteristic threshold decreases, while the corresponding steepness increases. Our observations remain valid if more complex sigmoid functions are used, thus reenforcing the importance of carefully adjusted benefits for high levels of public cooperation.

8 two-column pages, 8 figures; accepted for publication in Physical Review E

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Cited by in corpus (4)

• Coevolutionary dynamics via adaptive feedback in collective-risk social dilemma game
• Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game
• Frequency-dependent returns in nonlinear public goods games
• Evolutionary dynamics of continuous public goods games in structured populations