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Infection and immunization: A new class of evolutionary game dynamics

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  • Rota Bulò, Samuel
  • Bomze, Immanuel M.
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    Abstract

    Building upon a central paradigm of evolutionary game theory, namely the invasion barrier, we propose the new Infection and Immunization Dynamics (InfImmDyn), modelling a plausible adaptation process in a large population. For general games, this yields a novel refinement of the Nash equilibrium concept based on dynamical arguments, close in spirit to Nash's original "mass action" idea in his Ph.D. thesis. For partnership games, InfImmDyn exhibits a better asymptotic behavior compared to other popular procedures like Fictitious Play and Replicator Dynamics. We establish even support separation of InfImmDyn in finite time, which can never be achieved by any interior-point method like those mentioned above. In fact, this property has not yet been established for any other evolutionary game dynamics.

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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 71 (2011)
    Issue (Month): 1 (January)
    Pages: 193-211

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    Handle: RePEc:eee:gamebe:v:71:y:2011:i:1:p:193-211

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    Web page: http://www.elsevier.com/locate/inca/622836

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    Keywords: Revision protocol Evolutionary stability Equilibrium selection Fictitious play Replicator dynamics Best response Learning population games;

    References

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    1. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
    2. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    3. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
    4. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer, vol. 29(4), pages 571-595.
    5. 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.
    6. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    7. Bomze Immanuel M. & Weibull Jorgen W., 1995. "Does Neutral Stability Imply Lyapunov Stability?," Games and Economic Behavior, Elsevier, vol. 11(2), pages 173-192, November.
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    Cited by:
    1. Pietro Dindo & Jan Tuinstra, 2010. "A class of evolutionary models for participation games with negative feedback," LEM Papers Series 2010/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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