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Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

Marco A. Amaral1,*, Lucas Wardil2, Matjaž Perc3,4, and Jafferson K. L. da Silva1

  • 1Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil
  • 2Departamento de Fisica, Universidade Federal de Ouro Preto, Ouro Preto, 35400-000, MG, Brazil
  • 3Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
  • 4CAMTP–Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia

  • *marcoantonio.amaral@gmail.com
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Phys. Rev. E 93, 042304 – Published 6 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042304

Abstract

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is, in fact, strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

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Phys. Rev. E 93, 042304– Published 6 April, 2016
  • Received 19 February 2016

©2016 American Physical Society

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