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Evolutionary imitative dynamics with population-varying aspiration levels

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  • Sawa, Ryoji
  • Zusai, Dai

Abstract

We consider deterministic evolutionary dynamics under imitative revision protocols. We allow agents to have different aspiration levels in the imitative protocols where their aspiration levels are not observable to other agents. We show that the distribution of strategies becomes statistically independent of the aspiration level eventually in the long run. Thus, long-run properties of homogeneous imitative dynamics hold as well, despite heterogeneity in aspiration levels.

Suggested Citation

  • Sawa, Ryoji & Zusai, Dai, 2014. "Evolutionary imitative dynamics with population-varying aspiration levels," Journal of Economic Theory, Elsevier, vol. 154(C), pages 562-577.
    • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:562-577
    DOI: 10.1016/j.jet.2014.10.001
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    1. Colin Camerer & Linda Babcock & George Loewenstein & Richard Thaler, 1997. "Labor Supply of New York City Cabdrivers: One Day at a Time," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 407-441.
    2. Ulrich Berger, 2006. "A Generalized Model Of Best Response Adaptation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 45-66.
    3. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    4. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.
    5. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    6. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    7. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    8. Sandholm, William H., 2006. "Ross Cressman, Evolutionary Dynamics and Extensive Form Games, MIT Press, Cambridge, MA (2003)," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 136-140.
    9. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
    10. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 73-75, January.
    11. Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 527-538.
    12. Geroski, P. A., 2000. "Models of technology diffusion," Research Policy, Elsevier, vol. 29(4-5), pages 603-625, April.
    13. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    14. Dai Zusai, 2013. "Tempered Best Response Dynamics," DETU Working Papers 1301, Department of Economics, Temple University.
    15. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    16. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
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    Cited by:

    1. Dai Zusai, 2018. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," Papers 1805.04897, arXiv.org, revised May 2019.
    2. Dai Zusai, 2017. "Nonaggregable evolutionary dynamics under payoff heterogeneity," DETU Working Papers 1702, Department of Economics, Temple University.
    3. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.
    4. Alfio Giarlotta & Angelo Petralia, 2024. "Simon’s bounded rationality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 327-346, June.
    5. Dai Zusai, 2018. "Net gains in evolutionary dynamics: A unifying and intuitive approach to dynamic stability," Papers 1805.04898, arXiv.org, revised Oct 2023.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.

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    More about this item

    Keywords

    Learning; Imitation; Multiple populations; Aspiration level; Wright manifold;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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