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The effects of time-varying rewards on the evolution of cooperation

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Abstract

Understanding how cooperative behavior emerges within a population of autonomous individuals has been the focus of a great deal of research in biology, economics and more recently in the multi-agent systems domain. However, there are still many open questions. In this paper, we address some of these questions by investigating the effects of time-varying, non-symmetric rewards on the evolution of cooperation in the spatial Prisoner’s dilemma game. The rationale behind this approach is based on the notion that the associated payoffs from pursuing certain strategies do vary among members of real-world populations. In our model, agents with limited cognitive capacity play the game with their local neighbours. In addition to its game playing strategy, each agent has additional attributes that can be used to control the number of rounds of the game the agent actually participates in, as well as the magnitude of any rewards that it receives. Numerical simulations show that dynamic updates to payoff values induce a change in equilibrium cooperation levels. This suggests that heterogeneous payoff values and social diversity within a cost-benefit context are important factors in the promotion of cooperation in the spatial Prisoner’s dilemma game.

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References

  1. Axelrod R (1984) The evolution of cooperation. Basic Books, New York

    Google Scholar 

  2. Lindgren K, Nordahl MG (1994) Evolutionary dynamics of spatial games. Physica D 75:292–309

    Article  MATH  Google Scholar 

  3. Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359:826–829

    Article  Google Scholar 

  4. Nowak MA, Sigmund K (1992) Tit for tat in heterogeneous populations. Nature 355:250–252

    Article  Google Scholar 

  5. Fort H (2008) On evolutionary spatial heterogeneous games. Physica A 173(1):1613–1620

    Article  Google Scholar 

  6. Perc M, Szolnoki A (2008) Social diversity and promotion of cooperation in the spatial prisoner’s dilemma game. Phys Rev E 77:011904

    Google Scholar 

  7. Chong SY, Yao X (2006) Self-adapting payoff matrices in repeated interactions. Computational intelligence and games, IEEE symposium on, pp. 103–110

  8. Santos FC, Pacheco JM (2006) A new route to the evolution of cooperation. J Evol Biol 19(3):726–733

    Article  Google Scholar 

  9. Santos FC, Santos MD, Pacheco JM (2008) Social diversity promotes the emergence of cooperation in public goods games. Nature 454:213–216

    Article  Google Scholar 

  10. Kagel JH, Roth AE (1995) The handbook of experimental economics. Princeton University Press, Princeton

    Google Scholar 

  11. Lave LB (1965) Factors affecting cooperation in the prisoner’s dilemma. Behav Sci 10:26–38

    Article  Google Scholar 

  12. Boone C, De-Brabander B, van Witteloostuijn A (1999) The impact of personality on behavior in five prisoner’s dilemma games. J Econ Psychol 20:343–377

    Google Scholar 

  13. Johnson DP, Stopka P, Bell J (2002) Individual variation evades the prisoner’s dilemma. BMC Evol Biol 2(1):15

    Google Scholar 

  14. Turner PE, Chao L (2003) Escape from prisoner’s dilemma in RNA phage 6. Am Nat 161(3):497–505

    Article  Google Scholar 

  15. Fort H (2008) A minimal model for the evolution of cooperation through evolving heterogeneous games. Europhy Lett 81(408):97–216

    MathSciNet  Google Scholar 

  16. Tomochi M, Kono M (2002) Spatial prisoner’s dilemma games with dynamic payoff matrices. Phys Rev E 65(026112)

  17. Nowak MA (2006) Five rules for the evolution of cooperation. Science 314:1560–1563

    Article  Google Scholar 

  18. Axelrod R (1980) Evolution of cooperation. J Conflict Resolut 24:3–25

    Article  Google Scholar 

  19. Wooldridge M (2002) An introduction to multiagent systems. Wiley, Chichester

    Google Scholar 

  20. Kraines D, Kraines V (1989) Pavlov and the prisoner’s dilemma. Theory Decis 26:47–49

    Article  MathSciNet  Google Scholar 

  21. Hauert C (2001) Fundamental clusters in spatial 2 × 2 games. Proc R Soc Lond B 268:761–769

    Article  Google Scholar 

  22. Nowak MA, May RM (1993) The spatial dilemmas of evolution. Int J Bifurcat Chaos 3:35–78

    Article  MATH  MathSciNet  Google Scholar 

  23. Schweitzer F, Behera L, Muhlenbein H (2002) Evolution of cooperation in a spatial prisoner’s dilemma. Adv Complex Syst 5(2–3):269–299

    Article  MATH  MathSciNet  Google Scholar 

  24. Ohtsuki H, Hauert C, Lieberman E, Nowak MA (2006) A simple rule for the evolution of cooperation on graphs and social networks. Nature 441:502–505

    Article  Google Scholar 

  25. Szabo G, Fath G (2007) Evolutionary games on graphs. Phys Rep 446(4–6):97–216

    Article  MathSciNet  Google Scholar 

  26. Clements KC, Stephens DW (1995) Testing models of non-kin cooperation: mutualism and the prisoner’s dilemma. Anim Behav 50:527–535

    Article  Google Scholar 

  27. Wilensky U (2002) Modeling nature’s emergent patterns with multi-agent languages. In: Proceedings of EuroLogo, 2002. NetLogo is a cross-platform multi-agent programmable modeling environment. See http://www.ccl.northwestern.edu/netlogo/

  28. Noë R, Hammerstein P (1994) Biological markets: supply and demand determine the effect of partner choice in cooperation, mutualism and mating. Behav Ecol Sociobiol 35:1–11

    Article  Google Scholar 

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Correspondence to Golriz Rezaei.

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Rezaei, G., Kirley, M. The effects of time-varying rewards on the evolution of cooperation. Evol. Intel. 2, 207–218 (2009). https://doi.org/10.1007/s12065-009-0032-1

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