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A ‘Dual’-Improved Shortcut to the Long Run

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Abstract

I use the theories of duality and optimal branchings to find a necessary and sufficient characterization of stochastically stable limit sets (SSLS) that helps improve the radius -- modified coradius test of Ellison (2000). The improved shortcut I offer may permit the identification of SSLS when Ellison’s radius -- modified coradius test fails to identify any, or may be able to pinpoint the true SSLS in cases where Ellison’s test identifies only a superset. I also demonstrate precisely why the radius -- modified coradius test is not universally applicable and illuminate the connection between the modified coradius and the Lagrange multipliers of the optimal branching problem.

Suggested Citation

  • Kareen Rozen, 2008. "A ‘Dual’-Improved Shortcut to the Long Run," Cowles Foundation Discussion Papers 1643, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1643
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d16/d1643.pdf
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    References listed on IDEAS

    as
    1. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    2. Kevin Hasker, 2004. "The Emergent Seed : Simplifying the Analysis of Dynamic Evolution," Working Papers 0406, Department of Economics, Bilkent University.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    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.
    5. Troger, Thomas, 2002. "Why Sunk Costs Matter for Bargaining Outcomes: An Evolutionary Approach," Journal of Economic Theory, Elsevier, vol. 102(2), pages 375-402, February.
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    Cited by:

    1. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.

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    More about this item

    Keywords

    Evolutionary games; Stochastic stability; Optimal branchings; Extended radius; Extended coradius; Modified coradius;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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