IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v41y2013i2p233-247.html
   My bibliography  Save this article

Stochastic Evolutionary Game Dynamics and Their Selection Mechanisms

Author

Listed:
  • Xing Gao
  • Weijun Zhong
  • Shue Mei

Abstract

An underlying assumption of deterministic evolutionary game dynamics is that all individuals interact with each other in infinite populations, which seems unrealistic since in reality populations are always finite in size and even disturbed by stochastic effects and random drift. Developed in the context of finite populations and described by finite state Markov processes, stochastic evolutionary game dynamics have received much attention recently. However, the relationship between two types of evolutionary dynamics so far has failed to be thoroughly understood. In this paper, we establish several classes of selection mechanisms in large populations under which corresponding stochastic evolutionary dynamics approach the imitative dynamic (including the replicator dynamic), the impartial pairwise comparison dynamic (including the Smith dynamic) and the separable excess payoff dynamic (including the Brown–von Neumann–Nash dynamic) respectively in adjusted forms. In other words, we present intuitive interpretations from a statistical perspective for these deterministic dynamics by constructing their microscopic foundations in settings with finite but large populations. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Xing Gao & Weijun Zhong & Shue Mei, 2013. "Stochastic Evolutionary Game Dynamics and Their Selection Mechanisms," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 233-247, February.
    • Handle: RePEc:kap:compec:v:41:y:2013:i:2:p:233-247
    DOI: 10.1007/s10614-012-9320-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10614-012-9320-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10614-012-9320-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fishman, Michael A., 2008. "Asymmetric evolutionary games with non-linear pure strategy payoffs," Games and Economic Behavior, Elsevier, vol. 63(1), pages 77-90, May.
    2. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    3. 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.
    4. Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
    5. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    6. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    7. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    8. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    9. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    10. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    11. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Robert Jump, 2013. "Results on the Stability of a Simple Wage Posting Model," Studies in Economics 1319, School of Economics, University of Kent.
    2. Xinmin Liu & Kangkang Lin & Lei Wang & Hongkun Zhang, 2021. "Stochastic Evolutionary Game Analysis Between Special Committees and CEO: Incentive and Supervision," Dynamic Games and Applications, Springer, vol. 11(3), pages 538-555, September.
    3. Gao, Xing & Zhong, Weijun & Mei, Shue, 2013. "A game-theory approach to configuration of detection software with decision errors," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 35-43.
    4. Jianguo Ren & Yonghong Xu, 2014. "Modelling the Effects of Selection Temperature and Mutation on the Prisoner’s Dilemma Game on a Complete Oriented Star," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-9, October.
    5. Konstantin Avrachenkov & Vivek S. Borkar, 2019. "Metastability in Stochastic Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 9(2), pages 366-390, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
    3. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    4. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    5. Sylvain Sorin & Cheng Wan, 2016. "Finite composite games: Equilibria and dynamics," Post-Print hal-02885860, HAL.
    6. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    7. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    8. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    9. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    10. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
    11. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.
    12. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    13. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    14. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    15. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    16. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    17. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    18. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    19. Liu, Peng & Liao, Feixiong & Tian, Qiong & Huang, Hai-Jun & Timmermans, Harry, 2020. "Day-to-day needs-based activity-travel dynamics and equilibria in multi-state supernetworks," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 208-227.
    20. Xiaomei Zhao & Chunhua Wan & Jun Bi, 2019. "Day-to-Day Assignment Models and Traffic Dynamics Under Information Provision," Networks and Spatial Economics, Springer, vol. 19(2), pages 473-502, June.

    More about this item

    Keywords

    Stochastic evolutionary game dynamics; Finite population; Selection mechanisms; Coordination game; C73;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:41:y:2013:i:2:p:233-247. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.