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Step-by-Step Evolution with State-Dependent Mutations

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Thomas Norman () (Nuffield College, Oxford)

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Abstract

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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File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W8/Steps.pdf
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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2003-W08.

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Length: 16 pages
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Handle: RePEc:nuf:econwp:0308

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Web page: http://www.nuff.ox.ac.uk/economics/

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  1. David P. Myatt & Chris Wallace, 2002. "Adaptive Play by Idiosyncratic Agents," Economics Series Working Papers 089, University of Oxford, Department of Economics. [Downloadable!]
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  2. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July. [Downloadable!] (restricted)
  3. Adam Szeidl & In Ho Lee & Akos Valentinyi, 2001. "Contagion and State Dependent Mutations," IEHAS Discussion Papers 0104, Institute of Economics, Hungarian Academy of Sciences. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
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  5. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
  6. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
  7. William A. Brock & Steven N. Durlauf, 1995. "Discrete Choice with Social Interactions I: Theory," Working Papers 95-10-084, Santa Fe Institute.
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  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  9. Thomas Norman, 2003. "The Evolution of Coordination under Inertia," Economics Papers 2003-W06, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  10. In Ho Lee & Adam Szeidl & Akos Valentinyi, 2003. "Contagion and State Dependent Mutations," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 3(1), pages 1063-1063. [Downloadable!] (restricted)
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