IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9509001.html
   My bibliography  Save this paper

Evolutionary Equilibrium with Forward-Looking Players

Author

Listed:
  • Lawrence E. Blume

    (Cornell University)

Abstract

The stochastic evolutionary game literature is built on three behavioral postulates: ``noisy'' decisionmaking, myopic decisionmaking and random opportunities for choice (inertia). The role of noise is by now well- understood. This paper investigates the significance of the other two postulates. The model is the conventional evolutionary story, where a population of players is randomly matched against each other, and where strategy revision opportunities for each player arrive at random moments. But here players are assumed to have rational expectations about the evolution of play of their opponents, and choose revision policies to maximize the expected present value of the payoff stream. The dynamic programming problem each player solves is studied, and equilibrium is shown to exist. Not surprisingly, myopic play emerges as discount rates become large. More surprising is that, for any discount rate, myopic play also emerges as the arrival rate of strategy revision opportunities shrinks to~0. These results hold for any $K\times K$ symmetric game. For $2\times 2$ coordination games the effects of taking limits in the opposite direction is studied. When the noise term is small, if players are sufficiently patient or if the arrival rate of strategy revision opportunities is sufficiently large, the unique symmetric Markov equilibrium has each player always choosing the payoff- dominant strategy.

Suggested Citation

  • Lawrence E. Blume, 1995. "Evolutionary Equilibrium with Forward-Looking Players," Game Theory and Information 9509001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:9509001
    Note: 23 pages plus abstract and cover page, TeX file with one .eps file for a picture on the cover page.
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9509/9509001.pdf
    Download Restriction: no

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9509/9509001.ps.gz
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    2. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    3. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    4. Canning, D., 1990. "Social Equilibrium," Papers 150, Cambridge - Risk, Information & Quantity Signals.
    5. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    6. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    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. Blume, Lawrence, 2002. "Stigma and Social Control," Economics Series 119, Institute for Advanced Studies.
    2. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.

    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. Kandori, Michihiro & Serrano, Roberto & Volij, Oscar, 2008. "Decentralized trade, random utility and the evolution of social welfare," Journal of Economic Theory, Elsevier, vol. 140(1), pages 328-338, May.
    2. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
    3. Beggs, A.W., 2007. "Large deviations and equilibrium selection in large populations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 383-410, January.
    4. Oddvar M. Kaarbøe & Alexander F. Tieman, 0000. "Equilibrium Selection in Games with Macroeconomic Complementarities," Tinbergen Institute Discussion Papers 99-096/1, Tinbergen Institute.
    5. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
    7. Huw Dixon & Ernesto Somma, "undated". "Coordination and Equilibrium selection in mean defined supermodular games under payoff monotonic selection dynamics," Discussion Papers 99/37, Department of Economics, University of York.
    8. Ken Binmore & Larry Samuelson, 2010. "Muddling Through: Noisy Equilibrium Selection," Levine's Working Paper Archive 426, David K. Levine.
    9. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, October.
    10. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    11. Phillip M Johnson, 2002. "Essays on Capital Markets: Frictions and Social Forces," Levine's Working Paper Archive 618897000000000052, David K. Levine.
    12. Van Cleve, Jeremy & Lehmann, Laurent, 2013. "Stochastic stability and the evolution of coordination in spatially structured populations," Theoretical Population Biology, Elsevier, vol. 89(C), pages 75-87.
    13. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    14. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    15. Siegfried Berninghaus & Hans Haller & Alexander Outkin, 2006. "Neural networks and contagion," Revue d'économie industrielle, De Boeck Université, vol. 0(2), pages 11-11.
    16. Anthonisen, Niels, 1997. "On the Convergence of Beliefs within Populations in Games with Learning," Journal of Economic Theory, Elsevier, vol. 76(1), pages 169-184, September.
    17. Maryam Farboodi & Gregor Jarosch & Guido Menzio, 2016. "Intermediation as Rent Extraction," PIER Working Paper Archive 16-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2016.
    18. Guillaume Rocheteau & Pierre‐Olivier Weill, 2011. "Liquidity in Frictional Asset Markets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(s2), pages 261-282, October.
    19. Kiyotaki, Nobuhiro & Lagos, Ricardo & Wright, Randall, 2016. "Introduction to the symposium issue on money and liquidity," Journal of Economic Theory, Elsevier, vol. 164(C), pages 1-9.
    20. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:wpa:wuwpga:9509001. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.