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The projection dynamic and the geometry of population games

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  • Lahkar, Ratul
  • Sandholm, William H.

Abstract

The projection dynamic is an evolutionary dynamic for population games. It is derived from a model of individual choice in which agents abandon their current strategies at rates inversely proportional to the strategies' current levels of use. The dynamic admits a simple geometric definition, its rest points coincide with the Nash equilibria of the underlying game, and it converges globally to Nash equilibrium in potential games and in stable games.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:565-590
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    References listed on IDEAS

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    Cited by:

    1. Reinoud Joosten & Berend Roorda, 2011. "Attractive evolutionary equilibria," Papers on Economics and Evolution 2011-17, Philipps University Marburg, Department of Geography.
    2. repec:eee:gamebe:v:103:y:2017:i:c:p:41-66 is not listed on IDEAS
    3. Franke, Reiner, 2014. "Aggregate sentiment dynamics: A canonical modelling approach and its pleasant nonlinearities," Structural Change and Economic Dynamics, Elsevier, vol. 31(C), pages 64-72.
    4. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 147-161, October.
    5. repec:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0190-6 is not listed on IDEAS
    6. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    7. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    8. repec:spr:compst:v:74:y:2011:i:2:p:147-161 is not listed on IDEAS
    9. Pietro Dindo & Jan Tuinstra, 2011. "A Class of Evolutionary Models for Participation Games with Negative Feedback," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 267-300, March.
    10. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Philipps University Marburg, Department of Geography.
    11. Marc Harper & Dashiell Fryer, 2015. "Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex," Dynamic Games and Applications, Springer, vol. 5(3), pages 318-333, September.
    12. Rota Bulò, Samuel & Bomze, Immanuel M., 2011. "Infection and immunization: A new class of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 193-211, January.
    13. Fujishima, Shota, 2013. "Growth, agglomeration, and urban congestion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1168-1181.
    14. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    15. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    16. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    17. Lamantia, F. & Negriu, A. & Tuinstra, J., 2016. "Evolutionary Cournot competition with endogenous technology choice: (in)stability and optimal policy," CeNDEF Working Papers 16-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

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