Abstract
Classical theories explaining the evolution of cooperation often rely on the assumption that the involved players are symmetrically interacted. However, in reality almost all well-documented cooperation systems show that cooperative players are in fact asymmetrically interacted and that this dynamic may greatly affect the cooperative behavior of the involved players. Here, we developed several models based on the most well known spatial game of the Hawk-Dove game, while also considering the effects of asymmetric interaction. Such asymmetric games possess four kinds of strategies: cooperation or defection of strong player and cooperation or defection of weak player. Computer simulations showed that the probability of defection of the strong player decreases with decreasing the benefit to cost ratio, and that all kinds of strategy will be substituted by cooperation on behalf of the strong player if the benefit to cost ratio is sufficiently small. Moreover, weak players find it difficult to survive and the surviving weak players are mostly defectors, similar to the Boxed Pigs game. Interestingly, the patterns of kinds of strategies are chaotic or oscillate in some conditions with the related factors.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hanahan D, Weinberg R A. The hallmarks of cancer. Cell, 2000, 100: 57–70
Henrich J. Cooperation, punishment, and the evolution of human institutions. Science, 2006, 311: 60–61
Bronstein J L. The exploitation of mutualisms. Ecol Lett, 2001, 4: 277–287
Frank S A. Foundations of Social Evolution. Princeton, New Jersey: Princeton University Press, 1998
Wang R W, Sun B F, Zheng Q, et al. Asymmetric interaction and indeterminate fitness correlation between cooperative partners in the fig-fig wasp mutualism. J R Soc Interface, 2011, 8: 1487–1496
Hardin G. The tragedy of the commons. Science, 1968, 162: 1243–1248
West S A, Pen I, Griffin A S. Cooperation and competition between relatives. Science, 2002, 296: 72–75
Axelrod R. The Evolution of Cooperation. New York: Basic Books, 1984
Doebeli M, Knowlton N. The evolution of interspecific mutualisms. Proc Natl Acad Sci USA, 1998, 95: 8676–8680
Wang R W, Shi L, Ai S M, et al. Trade-off between reciprocal mutualists: Local resource availability-oriented interaction in fig/fig wasp mutualism. J Anim Ecol, 2008, 77: 616–623
Axelrod R, Hamilton W D. The evolution of cooperation. Science, 1981, 211: 1390–1396
Wang R W, Shi L. The evolution of cooperation in asymmetric systems. Sci China Life Sci, 2010, 53: 139–149
Wang R W, Ridley J, Sun B F, et al. Interference competition and high temperatures reduce the virulence of fig wasps and stabilize a fig-wasp mutualism. PLoS One, 2009, 4: e7802
Wang R W, Sun B F, Zheng Q. Diffusive coevolution and mutualism maintenance mechanisms in a fig-fig wasp system. Ecology, 2010, 91: 1308–1316
Pellmyr O, Huth C J. Evolutionary stability of mutualism between yuccas and yucca moths. Nature, 1994, 372: 257–260
Kiers E T, Rousseau R A, West S A, et al. Host sanctions and the legume-rhizobium mutualism. Nature, 2003, 425: 78–81
Reeve H K. Queen activation of lazy workers in colonies of the eusocial naked mole-rat. Nature, 1992, 358: 147–149
Clutton-Brock T H, Parker G A. Punishment in animal societies. Nature, 1995, 373: 209–216
Ratnieks F L W, Wenseleers T. Altruism in insect societies and beyond: Voluntary or enforced? Trends Ecol Evol, 2008, 23: 45–52
Ratnieks F L W, Wenseleers T. Policing insect societies. Science, 2005, 307: 54–56
He J Z, Wang R W, Christopher X J J, et al. Cooperation in an asymmetric volunteer’s dilemma game with relatedness. Chin Sci Bull, 2012, 57: 1972–1981
Pellmyr O, Leebens-Mack J. Reversal of mutualism as a mechanism for adaptive radiation in yucca moths. Am Nat, 2000, 156: S62–S76
Clutton-Brock T. Breeding together: Kin selection and mutualism in cooperative vertebrates. Science, 2002, 296: 69–72
Maynard Smith J. Evolution and the Theory of Games. Cambridge: Cambridge University Press, 1982
Wang R W, He J Z, Wang Y Q, et al. Asymmetric interaction will facilitate the evolution of cooperation. Sci China Life Sci, 2010, 53: 1041–1046
Nowak M A, May R M. Evolutionary games and spatial chaos. Nature, 1992, 359: 826–829
Nowak M, Sigmund K. A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner’s dilemma game. Nature, 1993, 364: 56–58
Nowak M A, Bonhoeffer S, May R M. More spatial games. Int J Bifurcation Chaos, 1994, 4: 33–56
Harsanyi J, Selten R. A general Theory of Equilibrium Selection in Gamesmit Press. Cambridge Massachussets: MIT Press, 1988
Hauert C, Doebeli M. Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature, 2004, 428: 643–646
Domjan M, Grau J W. The Principles of Learning and Behavior. Belmont: Thomson Brooks/Cole Publishing Co, 1998
MacLeod W B. Equity, efficiency, and incentives in cooperative teams. Adv Econom Anal Participatory Labor Managed Firms, 1988, 3: 5–23
Wakano J Y. Evolution of cooperation in spatial public goods games with common resource dynamics. J Theor Biol, 2007, 247: 616–622
Eric R. Games and Information: An Introduction to Game Theory. Oxford: Basil Blackwell, 2001
Mesterton-Gibbons M. Ecotypic variation in the asymmetric hawk-dove game: When is bourgeois an evolutionarily stable strategy? Evol Ecol, 1992, 6: 198–222
Neugebauer T, Poulsen A, Schram A. Fairness and reciprocity in the hawk-dove game. J Econ Behav Organ, 2008, 66: 243–250
Huia C, McGeoch M. Spatial patterns of prisoner’s dilemma game in metapopulations. Bull Math Biol, 2007, 69: 659–676
Author information
Authors and Affiliations
Corresponding authors
Additional information
This article is published with open access at Springerlink.com
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
He, J., Zhao, Y., Cai, H. et al. Spatial games and the maintenance of cooperation in an asymmetric Hawk-Dove game. Chin. Sci. Bull. 58, 2248–2254 (2013). https://doi.org/10.1007/s11434-013-5810-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11434-013-5810-6