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Generalized projection dynamics in evolutionary game theory

  • Reinoud Joosten
  • Berend Roorda
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    We introduce a new kind of projection dynamics by employing a ray-projection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global ray-projection dynamics we prove that every interior evolutionarily stable strategy is an asymptotically stable fixed point. We also show that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ several projections on a wider set of functions derived from the payoff structure. This yields an interesting class of so-called generalized projection dynamics which contains best-response, logit, replicator, and Brown-Von-Neumann dynamics among others.

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    Paper provided by Philipps University Marburg, Department of Geography in its series Papers on Economics and Evolution with number 2008-11.

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    Date of creation: Oct 2008
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    Handle: RePEc:esi:evopap:2008-11
    Contact details of provider: Postal: Deutschhausstrasse 10, 35032 Marburg
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    Web page: http://www.uni-marburg.de/fb19/
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    1. Tsakas, Elias & Voorneveld, Mark, 2007. "The target projection dynamic," SSE/EFI Working Paper Series in Economics and Finance 670, Stockholm School of Economics, revised 13 Aug 2007.
    2. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    3. Reinoud Joosten, 1996. "Deterministic evolutionary dynamics: a unifying approach," Journal of Evolutionary Economics, Springer, vol. 6(3), pages 313-324.
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    6. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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    8. Antonio Cabrales & Joel Sobel, 2010. "On the Limit Points of Discrete Selection Dynamics," Levine's Working Paper Archive 432, David K. Levine.
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    10. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
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    12. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
    13. Mark Voorneveld, 2006. "Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions," International Journal of Game Theory, Springer, vol. 34(1), pages 105-121, April.
    14. Sethi, Rajiv, 1998. "Strategy-Specific Barriers to Learning and Nonmonotonic Selection Dynamics," Games and Economic Behavior, Elsevier, vol. 23(2), pages 284-304, May.
    15. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    16. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
    17. J. Hofbauer & P. Schuster & K. Sigmund, 2010. "A Note on Evolutionary Stable Strategies and Game Dynamics," Levine's Working Paper Archive 441, David K. Levine.
    18. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
    19. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.
    20. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
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