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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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    1. George J. Mailath, 1998. "Corrigenda [Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory]," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1941-1941, December.
    2. Timothy N. Cason & Daniel Friedman & ED Hopkins, 2014. "Cycles and Instability in a Rock--Paper--Scissors Population Game: A Continuous Time Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 112-136.
    3. Ben Greiner, 2015. "Subject pool recruitment procedures: organizing experiments with ORSEE," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 1(1), pages 114-125, July.
    4. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
    5. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    6. James Pettit & Daniel Friedman & Curtis Kephart & Ryan Oprea, 2014. "Software for continuous game experiments," Experimental Economics, Springer;Economic Science Association, vol. 17(4), pages 631-648, December.
    7. Oprea, Ryan & Henwood, Keith & Friedman, Daniel, 2011. "Separating the Hawks from the Doves: Evidence from continuous time laboratory games," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2206-2225.
    8. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    9. Huck, Steffen & Jehiel, Philippe & Rutter, Tom, 2011. "Feedback spillover and analogy-based expectations: A multi-game experiment," Games and Economic Behavior, Elsevier, vol. 71(2), pages 351-365, March.
    10. Cressman R., 1995. "Evolutionary Game Theory with Two Groups of Individuals," Games and Economic Behavior, Elsevier, vol. 11(2), pages 237-253, November.
    11. Young, H. Peyton, 2011. "Commentary: John Nash and evolutionary game theory," Games and Economic Behavior, Elsevier, vol. 71(1), pages 12-13, January.
    12. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    13. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    14. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    15. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    16. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages 80-95, March.
    17. Mariana Blanco & Dirk Engelmann & Alexander Koch & Hans-Theo Normann, 2010. "Belief elicitation in experiments: is there a hedging problem?," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 412-438, December.
    18. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    19. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    20. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    21. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151.
    22. George J. Mailath, 1998. "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1347-1374, September.
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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 Külpmann & 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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