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Step-by-Step Evolution with State-Dependent Mutations

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This paper considers the extension of Ellison's (2000) "Radius-Modified Coradius" Theorem from the uniform-mutations case to a general stochastic setting. A modified theorem is presented, with a crucial role now played by the most probable evolutionary paths between states. The form of such paths is liable to change outside of the uniform mutations case, with concomitant effects on both long-run selection and expected waiting times. An algorithm for finding these paths is offered, and used to demonstrate the continued optimality of "step-by-step" evolution.

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  • Thomas Norman, "undated". "Step-by-Step Evolution with State-Dependent Mutations," Economics Papers 2003-W08, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0308
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    File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W8/Steps.pdf
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    1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    2. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Brock, W.A. & Durlauf, S.N., 1995. "Discrete Choice with Social Interactions I: Theory," Working papers 9521, Wisconsin Madison - Social Systems.
    5. Thomas Norman, 2003. "The Evolution of Coordination under Inertia," Economics Papers 2003-W06, Economics Group, Nuffield College, University of Oxford.
    6. Lee In Ho & Szeidl Adam & Valentinyi Akos, 2003. "Contagion and State Dependent Mutations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-29, February.
    7. 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.
    8. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    9. Myatt, David P. & Wallace, Chris C., 2004. "Adaptive play by idiosyncratic agents," Games and Economic Behavior, Elsevier, vol. 48(1), pages 124-138, July.
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