IDEAS home Printed from https://ideas.repec.org/p/els/esrcls/036.html
   My bibliography  Save this paper

Muddling Through: Moisy Equlibrium Selection

Author

Listed:
  • Ken Binmore
  • Larry Samuelson

Abstract

This paper examines an evolutionary model in which the primary source of noise that moves the model between equilibria is not arbitrarily improbvable mutations but mistakes in learning. We model strategy selection as a birth-death process, allowing us to and a simple, closed-form solution for the stationary distribution of the model even though we take the noise to be bounded away from zero. We examine equilibrium selection by considering the limiting case as the population gets large, eliminating aggregate noise from the model. Conditions are established under which the risk-dominant equilibrium in a 2 x 2 game is selected by the model as well as conditions under which the payoff-dominant equilibrium is selected.

Suggested Citation

  • Ken Binmore & Larry Samuelson, "undated". "Muddling Through: Moisy Equlibrium Selection," ELSE working papers 036, ESRC Centre on Economics Learning and Social Evolution.
    • Handle: RePEc:els:esrcls:036
    as

    Download full text from publisher

    File URL: ftp://ftp.repec.org/RePEc/els/esrcls/muddling.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 605-639.
    4. 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.
    5. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Consumer Theory," Discussion Papers 1025, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Gilboa, Itzhak & Schmeidler, David, 1996. "Case-Based Optimization," Games and Economic Behavior, Elsevier, vol. 15(1), pages 1-26, July.
    9. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
    10. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
    11. Binmore, K. & Samuelson, L. & Vaughan, R., 1993. "Musical Chairs: Modelling Noisy Evolution," Working papers 9324, Wisconsin Madison - Social Systems.
    12. Robson, Arthur J., 1996. "A Biological Basis for Expected and Non-expected Utility," Journal of Economic Theory, Elsevier, vol. 68(2), pages 397-424, February.
    13. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    14. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    15. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    16. Bendor, J. & Mookherjee, D. & Ray, D., 1994. "Aspirations, adaptive learning and cooperation in repeated games," Discussion Paper 1994-42, Tilburg University, Center for Economic Research.
    17. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    Full references (including those not matched with items on IDEAS)

    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. Ken Binmore & Larry Samuelson, 2010. "Muddling Through: Noisy Equilibrium Selection," Levine's Working Paper Archive 426, David K. Levine.
    2. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    3. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, University Library of Munich, Germany.
    4. 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.
    5. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    6. de Vries, F.P., 1999. "The Behavioral Firm and Its Internal Game : Evolutionary Dynamics of Decision Making," Other publications TiSEM 81ac857a-7637-49d8-a52e-3, Tilburg University, School of Economics and Management.
    7. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine.
    9. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.
    10. Ilan Eshel & Larry Samuelson & Avner Shaked, "undated". "Altruists Egoists and Hooligans in a Local Interaction Model," ELSE working papers 005, ESRC Centre on Economics Learning and Social Evolution.
    11. Amit Pazgal, 1995. "Satisficing Leads to Cooperation in Mutual Interests Games," Discussion Papers 1126, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Napel, Stefan, 2003. "Aspiration adaptation in the ultimatum minigame," Games and Economic Behavior, Elsevier, vol. 43(1), pages 86-106, April.
    13. Desirée Desierto, 2012. "Imitation Dynamics with Spatial Poisson-Distributed Review and Mutation Rates," UP School of Economics Discussion Papers 201204, University of the Philippines School of Economics.
    14. Roland Pongou & Roberto Serrano, 2009. "A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS," Working Papers 2009-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    15. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    16. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    17. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2014. "Imitation and the role of information in overcoming coordination failures," Games and Economic Behavior, Elsevier, vol. 87(C), pages 397-411.
    18. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    19. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    20. 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.

    More about this item

    Keywords

    Equilibrium selection; Evolutionary games; Mutations; Risk dominance.;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

    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:els:esrcls:036. 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: s. malkani (email available below). General contact details of provider: https://edirc.repec.org/data/elucluk.html .

    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.