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Muddling Through: Moisy Equlibrium Selection

  • Ken Binmore
  • Larry Samuelson
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    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.

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    File URL: ftp://ftp.repec.org/RePEc/els/esrcls/muddling.pdf
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    Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 036.

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    Handle: RePEc:els:esrcls:036
    Contact details of provider: Web page: http://else.econ.ucl.ac.uk/
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    1. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
    2. 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.
    3. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Scholarly Articles 3196332, Harvard University Department of Economics.
    4. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
    5. Ken Binmore & Larry Samuelson, 1994. "Muddling Through:Noisy Equilibrium Selection," Game Theory and Information 9403005, EconWPA, revised 29 Mar 1994.
    6. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    7. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
    8. Bendor, J. & Mookherjee, D. & Ray, D., 1994. "Aspirations, Adaptive Learning and Cooperation in Reapeted Games," Papers 27, Boston University - Department of Economics.
    9. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    10. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    11. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 69(1), pages 99-118.
    12. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    13. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Optimization," Discussion Papers 1039, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Binmore, K. & Samuelson, L. & Vaughan, R., 1993. "Musical Chairs: Modelling Noisy Evolution," Working papers 9324, Wisconsin Madison - Social Systems.
    15. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Consumer Theory," Discussion Papers 1025, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. 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.
    17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    18. Paul R. Milgrom, 1979. "Good Nevs and Bad News: Representation Theorems and Applications," Discussion Papers 407R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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