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Imitative Behavior in a Two-Population Model

  • Elvio Accinelli
  • Juan Gabriel Brida
  • Edgar J. Sanchez Carrera
Chapter
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)

Abstract

We study an evolutionary game with two asymmetric populations where agents from each population are randomly paired with members of the other population. We present two imitation models. In the first model, dissatisfaction drives imitation. In the second model, agents imitate the successful. In the first model, we use a simple reviewing rule, while in the second model we use a proportional imitation rule where switching depends on agents comparing their payoffs to others’ payoffs. We show that such imitative behavior can be approximated by a replicator dynamic system. We characterize the evolutionarily stable strategies for a two asymmetric populations normal form game and we show that a mixed strategy is evolutionary stable if and only if it is a strict Nash equilibrium. We offer one clear conclusion: whom an agent imitates is more important than how an agent imitates.

Keywords

Nash Equilibrium Equilibrium Point Mixed Strategy Pure Strategy Stable Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alos-Ferrer, Weidenholzer, S.: Imitation, Local Interactions and Efficiency. Economics Letters 93(2), 163–168 (2006)Google Scholar
  2. 2.
    Apesteguia, J., Huck, S., Oechssler, J.: Imitation-theory and experimental evidence. Journal of Economic Theory 136, 217–235 (2007)MATHCrossRefGoogle Scholar
  3. 3.
    Björnerstedt, J., Weibull, J.: Nash equilibrium and evolution by imitation. In: Arrow, K. et al. (eds.) The Rational Foundations of Economic Behaviour. Macmillan, Hampshire (1996)Google Scholar
  4. 4.
    Hines, W.G.S.: Three Characterizations of Population Strategy Stability. Journal of Applied Probability 17, 333–340 (1980)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (2002)Google Scholar
  6. 6.
    Rice, S.H.: Evolutionary Theory: Mathematical and Conceptual Foundations. Sinauer Associates, Sunderland (2004)Google Scholar
  7. 7.
    Maynard Smith, J.: The theory of games and the evolution of animal conflict. Journal of Theoretical Biology 47, 209–222 (1974)Google Scholar
  8. 8.
    Samuelson, L., Zhang, J.: Evolutionary Stability in Asymmetric Games. Journal of Economic Theory 57, 363–391 (1992)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Schlag, K.H.: Why Imitate, and if so, How? A Boundedly Rational Approach to Multi-Armed Bandits. Journal of Economic Theory 78(1), 130–156 (1998)MATHMathSciNetGoogle Scholar
  10. 10.
    Schlag, K.H.: Which One Should I Imitate. Journal of Mathematical Economics 31(4), 493–522 (1999)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Taylor, P.: Evolutionarily stable strategies with two types of player. Journal of Applied Probability 16, 76–83 (1979)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Vega-Redondo, F.: The evolution of Walrasian behavior. Econometrica 65, 375–384 (1997)MATHCrossRefGoogle Scholar
  13. 13.
    Vega-Redondo, F.: Evolution, Games, and Economic Behavior. Oxford University Press, Oxford, New York (1996)CrossRefGoogle Scholar
  14. 14.
    Weibull, W.J.: Evolutionary Game Theory. MIT, Cambridge (1995)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Elvio Accinelli
    • 1
  • Juan Gabriel Brida
    • 2
  • Edgar J. Sanchez Carrera
    • 3
  1. 1.Facultad de EconomiaUASLPSan Luis PotosíMexico
  2. 2.School of EconomicsFree University of BozenBolzanoItaly
  3. 3.Department of EconomicsUniversity of SienaSienaItaly

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