IDEAS home Printed from https://ideas.repec.org/p/vie/viennp/vie0008.html

Finite Population Dynamics and Mixed Equilibria

Author

Abstract

This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered and combined with different assumptions about the speed of adjustment. It is found that specific refinements of mixed Nash equilibria serve to identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 x 2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

Suggested Citation

  • Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers vie0008, University of Vienna, Department of Economics.
    • Handle: RePEc:vie:viennp:vie0008
    as

    Download full text from publisher

    File URL: https://papersecon.univie.ac.at/RePEc/vie/viennp/vie0008.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    2. John F. Nash Jr, 1996. "Essays on Game Theory," Books, Edward Elgar Publishing, number 1089.
    3. Carlos Alós-Ferrer, 2000. "Learning, Memory, and Inertia," Vienna Economics Papers 0003, University of Vienna, Department of Economics.
    4. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    5. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
    6. Alos-Ferrer, C., 1998. "Individual Randomness in Economic Models with a Continuum Agents," Papers 9807, Washington St. Louis - School of Business and Political Economy.
    7. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
    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. is not listed on IDEAS
    2. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    3. van Hoesel, C.P.M. & van der Kraaij, A.F. & Mannino, C. & Oriolo, G. & Bouhtou, M., 2003. "Polynomial cases of the tarification problem," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Carlos Alós-Ferrer & Georg Kirchsteiger, 2015. "Learning and market clearing: theory and experiments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 203-241, October.
    5. Yaroslav Rosokha & Xinxin Lyu & Denis Tverskoi & Sergey Gavrilets, 2026. "Evolution of cooperation in the indefinitely repeated collective action with a contest for power," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 81(1), pages 453-483, February.
    6. Alos-Ferrer, C. & Kirchsteiger, G., 2003. "Does learning lead to coordination on market clearing institutions," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2006. "Imitation, local interactions, and efficiency," Economics Letters, Elsevier, vol. 93(2), pages 163-168, November.
    8. Carlos Alós-Ferrer & Georg Kirchsteiger & Markus Walzl, 2010. "On the Evolution of Market Institutions: The Platform Design Paradox," Economic Journal, Royal Economic Society, vol. 120(543), pages 215-243, March.
    9. Thomas Norman, 2010. "Cycles versus equilibrium in evolutionary games," Theory and Decision, Springer, vol. 69(2), pages 167-182, August.

    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. Carlos Alós-Ferrer, 2003. "Finite Population Dynamics and Mixed Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 263-290.
    2. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    3. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    4. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    5. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    6. Hsiao-Chi Chen & Yunshyong Chow & Li-Chau Wu, 2013. "Imitation, local interaction, and coordination," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1041-1057, November.
    7. Karavaev, Andrei, 2008. "A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings," MPRA Paper 7445, University Library of Munich, Germany.
    8. H. Peyton Young, 2007. "Social Norms," Economics Series Working Papers 307, University of Oxford, Department of Economics.
    9. Tanaka, Yasuhito, 2000. "A finite population ESS and a long run equilibrium in an n players coordination game," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 195-206, March.
    10. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    11. Bilancini, Ennio & Boncinelli, Leonardo, 2022. "The evolution of conventions in the presence of social competition," Games and Economic Behavior, Elsevier, vol. 133(C), pages 50-57.
    12. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, vol. 1(4), pages 1-35, November.
    13. Molzon, Robert & Puzzello, Daniela, 2010. "On the observational equivalence of random matching," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1283-1301, May.
    14. Ianni, Antonella, 2001. "Learning correlated equilibria in population games," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 271-294, November.
    15. Kim, Chongmin & Wong, Kam-Chau, 2010. "Long-run equilibria with dominated strategies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 242-254, January.
    16. Fei Shi, 2015. "Long-run technology choice with endogenous local capacity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 377-399, June.
    17. Thierry Vignolo, 2010. "Imitation and selective matching in reputational games," Journal of Evolutionary Economics, Springer, vol. 20(3), pages 395-412, June.
    18. 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.
    19. Desiree A. Desierto, 2008. "The Dynamics of Economic Integration," DEGIT Conference Papers c013_029, DEGIT, Dynamics, Economic Growth, and International Trade.
    20. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:vie:viennp:vie0008. 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: Paper Administrator (email available below). General contact details of provider: https://econ.univie.ac.at/ .

    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.