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Equilibrium selection with coupled populations in hawk–dove games: Theory and experiment in continuous time

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  • Benndorf, Volker
  • Martínez-Martínez, Ismael
  • Normann, Hans-Theo

Abstract

Standard one- and two-population models for evolutionary games are the limit cases of a uniparametric family combining intra- and intergroup interactions. Our setup interpolates between both extremes with a coupling parameter κ. For the example of the hawk–dove game, we analyze the replicator dynamics of the coupled model. We confirm the existence of a bifurcation in the dynamics of the system and identify three regions for equilibrium selection, one of which does not appear in common one- and two-population models. We also design a continuous-time experiment, exploring the dynamics and the equilibrium selection. The data largely confirm the theory.

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  • Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2016. "Equilibrium selection with coupled populations in hawk–dove games: Theory and experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 165(C), pages 472-486.
    • Handle: RePEc:eee:jetheo:v:165:y:2016:i:c:p:472-486
    DOI: 10.1016/j.jet.2016.06.003
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    Cited by:

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    3. Benndorf, Volker & Martínez-Martínez, Ismael, 2017. "Perturbed best response dynamics in a hawk–dove game," Economics Letters, Elsevier, vol. 153(C), pages 61-64.
    4. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    5. Zhao, Shuchen, 2021. "Taking turns in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 257-279.
    6. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.
    7. Blázquez, Mario & Koptyug, Nikita, 2022. "Equilibrium Selection in Hawk-Dove Games," Discussion Papers 2022/12, Norwegian School of Economics, Department of Business and Management Science.
    8. Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2021. "Games with coupled populations: An experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 195(C).
    9. Philipp Kuelpmann & Christoph Kuzmics, 2019. "On the Predictive Power of Theories of One-Shot Play," Graz Economics Papers 2019-09, University of Graz, Department of Economics.
    10. Céline Bonnet & Jan Philip Schain, 2020. "An Empirical Analysis Of Mergers: Efficiency Gains And Impact On Consumer Prices," Journal of Competition Law and Economics, Oxford University Press, vol. 16(1), pages 1-35.
    11. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2021. "An Experimental Investigation of Price Dispersion and Cycles," Journal of Political Economy, University of Chicago Press, vol. 129(3), pages 789-841.
    12. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2021. "Sampling dynamics and stable mixing in hawk-dove games," Papers 2107.08423, arXiv.org, revised Jun 2022.
    13. Philip J. Grossman & Youngseok Park & Jean Paul Rabanal & Olga A. Rud, 2019. "Gender differences in an endogenous timing conflict game," Working Papers 141, Peruvian Economic Association.
    14. Arigapudi, Srinivas & Heller, Yuval & Schreiber, Amnon, 2021. "Sampling Dynamics and Stable Mixing in Hawk–Dove Games," MPRA Paper 108819, University Library of Munich, Germany.
    15. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.

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    More about this item

    Keywords

    Evolutionary game theory; Experiment in continuous time; Hawk–dove game; Replicator dynamics;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

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