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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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    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
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    1. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Consumer Theory," Discussion Papers 1025, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. 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.
    3. Gilboa, Itzhak & Schmeidler, David, 1996. "Case-Based Optimization," Games and Economic Behavior, Elsevier, vol. 15(1), pages 1-26, July.
    4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    5. G. Ellison & D. Fudenberg, 2010. "Rules of Thumb for Social Learning," Levine's Working Paper Archive 435, David K. Levine.
    6. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
    7. 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.
    8. Ken Binmore & Larry Samuelson, 1994. "Muddling Through:Noisy Equilibrium Selection," Game Theory and Information 9403005, EconWPA, revised 29 Mar 1994.
    9. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    10. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    12. 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.
    13. 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.
    14. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
    15. repec:att:wimass:9324 is not listed on IDEAS
    16. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
    17. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
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