Artificial Life and Robotics

, Volume 14, Issue 3, pp 414–417 | Cite as

Evolution of cooperative behavior among heterogeneous agents with different strategy representations in an iterated prisoner’s dilemma game

  • Hiroyuki Ohyanagi
  • Yoshihiko Wakamatsu
  • Yusuke Nakashima
  • Yusuke Nojima
  • Hisao Ishibuchi
Original Article

Abstract

The iterated prisoner’s dilemma (IPD) game has frequently been used to examine the evolution of cooperative behavior among agents. When the effect of representation schemes of IPD game strategies was examined, the same representation scheme was usually assigned to all agents. That is, in the literature, a population of homogeneous agents was usually used in computational experiments. In this article, we focus on a slightly different situation where every agent does not necessarily use the same representation scheme. That is, a population can be a mixture of heterogeneous agents with different representation schemes. In computational experiments, we used binary strings of different lengths (i.e., three-bit and five-bit strings) to represent IPD game strategies. We examined the evolution of cooperative behavior among heterogeneous agents in comparison with the case of homogeneous ones for the standard IPD game with typical payoff values of 0, 1, 3, and 5. Experimental results showed that the evolution of cooperative behavior was slowed down by the use of heterogeneous agents. It was also demonstrated that a faster evolution of cooperative behavior is achieved among majority agents than among minority ones in a heterogeneous population.

Key words

Iterated prisoner’s dilemma (IPD) game Evolution of cooperative behavior Evolution of game strategies Genetic algorithms Coding schemes 

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References

  1. 1.
    Axelrod R (1987) The evolution of strategies in the Iterated prisoner’s dilemma. In: Davis L (ed) Genetic algorithms and simulated annealing. Morgan Kaufmann, Los Altos, pp 32–41Google Scholar
  2. 2.
    Lindgren K (1991) Evolution phenomena in simple dynamics. In: Langton CG, Taylor C, Farmer JD, et al (eds) Artificial Life II. Addison-Wesley, Reading, pp 295–312Google Scholar
  3. 3.
    Fogel DB (1993) Evolving behaviors in the iterated prisoner’s dilemma. Evolut Comput 1:77–97CrossRefGoogle Scholar
  4. 4.
    Darwen P, Yao X (1996) Automatic modularisation by speciation. Proceedings of the 3rd IEEE International Conference on Evolutionary Computation, IEEE, New York, pp 88–93CrossRefGoogle Scholar
  5. 5.
    Crowley PH, Provencher L, Sloane S, et al (1996) Evolving cooperation: the role of individual recognition. BioSystems 37:49–66CrossRefGoogle Scholar
  6. 6.
    Ashlock D, Smucker MD, Stanley EA, et al (1996) Preferential partner selection in an evolutionary study of prisoner’s dilemma. BioSystems 37:99–125CrossRefGoogle Scholar
  7. 7.
    Bankes S (1994) Exploring the foundations of artificial societies: experiments in evolving solutions to iterated N-player prisoner’s dilemma. In: Brooks RA, Maes P (eds) Artificial Life IV. MIT, Cambridge, pp 237–242Google Scholar
  8. 8.
    Yao X, Darwen P (1994) An experimental study of N-person iterated prisoner’s dilemma games. Informatica 18:435–450MATHGoogle Scholar
  9. 9.
    Nowak MA, May RM, Sigmund K (1995) The arithmetics of mutual help. Sci Am 272:76–81CrossRefGoogle Scholar
  10. 10.
    Lloyd AL (1995) Computing bouts of the prisoner’s dilemma. Sci Am 272:80–83Google Scholar
  11. 11.
    Grim P (1996) Spatialization and greater generosity in the stochastic prisoner’s dilemma. BioSystems 37:3–17CrossRefGoogle Scholar
  12. 12.
    Brauchli K, Killingback T, Doebeli M (1999) Evolution of cooperation in spatially structured populations. J Theor Biol 200:405–417CrossRefGoogle Scholar
  13. 13.
    Ishibuchi H, Namikawa N (2005) Evolution of cooperative behavior in the iterated prisoner’s dilemma under random pairing in game playing. Proceedings of the 2005 IEEE Congress on Evolutionary Computation, pp 2637–2644Google Scholar
  14. 14.
    Ishibuchi H, Namikawa N (2005) Evolution of iterated prisoner’s dilemma game strategies in structured demes under random pairing in game playing. IEEE Trans Evolut Comput 9:552–561CrossRefGoogle Scholar
  15. 15.
    Dugatkin LA (1997) Cooperation among animals — an evolutionary perspective. Oxford University Press, New YorkGoogle Scholar
  16. 16.
    Ashlock D, Kim EY, Leahy N (2006) Understanding representational sensitivity in the iterated prisoner’s dilemma with fingerprints. IEEE Trans Syst Man Cybern Part C 36:464–475CrossRefGoogle Scholar
  17. 17.
    Ashlock D, Kim EY (2008) Fingerprinting: visualization and automatic analysis of prisoner’s dilemma strategies. IEEE Trans Evolut Comput 12:647–659CrossRefGoogle Scholar

Copyright information

© International Symposium on Artificial Life and Robotics (ISAROB). 2009

Authors and Affiliations

  • Hiroyuki Ohyanagi
    • 1
  • Yoshihiko Wakamatsu
    • 1
  • Yusuke Nakashima
    • 1
  • Yusuke Nojima
    • 1
  • Hisao Ishibuchi
    • 1
  1. 1.Department of Computer Science and Intelligent Systems, Graduate School of EngineeringOsaka Prefecture UniversitySakai, OsakaJapan

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