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The Continuous Time Infection–Immunization Dynamics

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  • Reinhard Ullrich

    (University of Vienna)

Abstract

Recently a new evolutionary game dynamics, the Infection–Immunization Dynamics,has been introduced for discrete time. In this paper a continuous time version of this model is derived and the existence and structure of solutions is analysed. This is a very challenging task, since standard technique existence theorems for Differential Inclusions do not hold in general. An extended solution concept, the notion of Krasovsky solutions, can be applied though. Some stability results are stated and discussed.

Suggested Citation

  • Reinhard Ullrich, 2017. "The Continuous Time Infection–Immunization Dynamics," Dynamic Games and Applications, Springer, vol. 7(3), pages 492-506, September.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0191-5
    DOI: 10.1007/s13235-016-0191-5
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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. 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.
    3. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Evolutionary stability; Equilibrium selection; Infection–Immunization Dynamics; Differential inclusion; Best response;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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