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Sophisticated imitation in cyclic games

Author

Listed:
  • Josef Hofbauer

    (Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria)

  • Karl H. Schlag

    (Economics Department, European University Institute, Via dei Roccettini 9, 50016 San Domenico di Fiesole, Italy)

Abstract

Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic $2\times 2$ game such as Matching Pennies. Between matching rounds, individuals sometimes change their strategy after observing a finite sample of other outcomes within their population. Individuals from the same population follow the same behavioral rule. In the resulting discrete time dynamics the unique Nash equilibrium is unstable. However, for sample sizes greater than one, we present an imitation rule where long run play cycles closely around the equilibrium.

Suggested Citation

  • Josef Hofbauer & Karl H. Schlag, 2000. "Sophisticated imitation in cyclic games," Journal of Evolutionary Economics, Springer, vol. 10(5), pages 523-543.
    • Handle: RePEc:spr:joevec:v:10:y:2000:i:5:p:523-543
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    Citations

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    Cited by:

    1. Offerman, Theo & Schotter, Andrew, 2009. "Imitation and luck: An experimental study on social sampling," Games and Economic Behavior, Elsevier, vol. 65(2), pages 461-502, March.
    2. Güth Werner & Kliemt Hartmut & Peleg Bezalel, 2000. "Co-evolution of Preferences and Information in Simple Games of Trust," German Economic Review, De Gruyter, vol. 1(1), pages 83-110, February.
    3. Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
    4. Enrique Urbano Arellano & Xinyang Wang, 2023. "Social Learning of General Rules," Papers 2310.15861, arXiv.org.
    5. Lipatov, Vilen, 2003. "Evolution of Tax Evasion," MPRA Paper 966, University Library of Munich, Germany, revised 06 Dec 2005.
    6. Luckraz, Shravan, 2013. "On innovation cycles in a finite discrete R&D game," Economic Modelling, Elsevier, vol. 30(C), pages 510-513.
    7. Martin Posch, 2001. "Win Stay, Lose Shift or Imitatation – Only the Choice of Peers Counts," Vienna Economics Papers vie0109, University of Vienna, Department of Economics.
    8. Ana B. Ania, 2000. "Learning by Imitation when Playing the Field," Vienna Economics Papers vie0005, University of Vienna, Department of Economics.
    9. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
    10. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
    11. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    12. Alanyali, Murat, 2010. "A note on adjusted replicator dynamics in iterated games," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 86-98, January.
    13. Ana B. Ania, 2000. "Learning by Imitation when Playing the Field," Vienna Economics Papers 0005, University of Vienna, Department of Economics.
    14. Karl H. Schlag, 2022. "Social Learning between Groups: Imitation and the Role of Experience," Games, MDPI, vol. 13(5), pages 1-14, September.
    15. Hwang, Sung-Ha & Rey-Bellet, Luc, 2020. "Strategic decompositions of normal form games: Zero-sum games and potential games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 370-390.

    More about this item

    Keywords

    Strictly improving - Matching pennies game - Replicator dynamics - Limit cycle - Discretization;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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