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

Xiaojie Chen, Attila Szolnoki, Matjaž Perc, and Long Wang
Phys. Rev. E 85, 066133 – Published 29 June 2012

Abstract

Cooperation and defection may be considered to be 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.

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  • Received 17 February 2012

DOI:https://doi.org/10.1103/PhysRevE.85.066133

©2012 American Physical Society

Authors & Affiliations

Xiaojie Chen1,*, Attila Szolnoki2, Matjaž Perc3, and Long Wang4

  • 1Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria
  • 2Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, Hungary
  • 3Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
  • 4State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China

  • *chenx@iiasa.ac.at

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Vol. 85, Iss. 6 — June 2012

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