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Infection and immunization: A new class of evolutionary game dynamics

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  • Rota Bulò, Samuel
  • Bomze, Immanuel M.

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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  • 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.
    • Handle: RePEc:eee:gamebe:v:71:y:2011:i:1:p:193-211
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    References listed on IDEAS

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    1. 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.
    2. Robert J. Leonard, 1995. "From Parlor Games to Social Science: Von Neumann, Morgenstern, and the Creation of Game Theory, 1928-1994," Journal of Economic Literature, American Economic Association, vol. 33(2), pages 730-761, June.
    3. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    4. 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.
    5. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    6. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    7. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    8. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    9. 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.
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    Cited by:

    1. Reinhard Ullrich, 2017. "The Continuous Time Infection–Immunization Dynamics," Dynamic Games and Applications, Springer, vol. 7(3), pages 492-506, September.
    2. Bomze, Immanuel M. & Gabl, Markus & Maggioni, Francesca & Pflug, Georg Ch., 2022. "Two-stage stochastic standard quadratic optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 21-34.
    3. 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.
    4. Immanuel M. Bomze & Werner Schachinger & Reinhard Ullrich, 2018. "The Complexity of Simple Models—A Study of Worst and Typical Hard Cases for the Standard Quadratic Optimization Problem," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 651-674, May.
    5. Stephenson, Daniel, 2019. "Coordination and evolutionary dynamics: When are evolutionary models reliable?," Games and Economic Behavior, Elsevier, vol. 113(C), pages 381-395.
    6. Elena Gubar & Vladislav Taynitskiy & Quanyan Zhu, 2018. "Optimal Control of Heterogeneous Mutating Viruses," Games, MDPI, vol. 9(4), pages 1-18, December.
    7. Schimit, P.H.T. & Santos, B.O. & Soares, C.A., 2015. "Evolution of cooperation in Axelrod tournament using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 204-217.
    8. Rota Bulò, Samuel & Pelillo, Marcello, 2017. "Dominant-set clustering: A review," European Journal of Operational Research, Elsevier, vol. 262(1), pages 1-13.

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