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Muddling Through: Moisy Equlibrium Selection

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  • Ken Binmore
  • Larry Samuelson
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    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.

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    File URL: ftp://ftp.repec.org/RePEc/els/esrcls/muddling.pdf
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    Bibliographic Info

    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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    Related research

    Keywords: Equilibrium selection; Evolutionary games; Mutations; Risk dominance.;

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    References

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    1. D. Fudenberg & C. Harris, 2010. "Evolutionary Dynamics with Aggregate Shocks," Levine's Working Paper Archive 496, David K. Levine.
    2. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. 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.
    4. repec:att:wimass:9410 is not listed on IDEAS
    5. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
    6. Binmore, K. & samuelson, L., 1996. "Muddling Through : Noisy Equilibrium Section," Working papers 9410r, Wisconsin Madison - Social Systems.
    7. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
    8. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
    10. Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
    11. repec:att:wimass:9324 is not listed on IDEAS
    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. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Optimization," Discussion Papers 1039, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. 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.
    15. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    16. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    18. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Consumer Theory," Discussion Papers 1025, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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