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Payoff Dependent Dynamics and Coordination Games

Author

Listed:
  • Hwang, Sung-Ha
  • Newton, Jonathan
Abstract
This paper considers populations of agents whose behavior when playing some underlying game is governed by perturbed best (or better) response dynamics with perturbation probabilities that depend log-linearly on payoffs, a class that includes the logit choice rule. A convention is a state at which every agent plays a strategy that corresponds to the same strict Nash equilibrium of the underlying game. For coordination games with zero payoffs off-diagonal, it is shown that the difficulty of leaving the basin of attraction of a convention can be well approximated by only considering paths of transitions on which an identical perturbation repeatedly affects one of the populations.

Suggested Citation

  • Hwang, Sung-Ha & Newton, Jonathan, 2016. "Payoff Dependent Dynamics and Coordination Games," Working Papers 2016-12, University of Sydney, School of Economics.
  • Handle: RePEc:syd:wpaper:2016-12
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    File URL: http://econ-wpseries.com/2016/201612-03.pdf
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    References listed on IDEAS

    as
    1. Lundberg, Shelly & Pollak, Robert A, 1993. "Separate Spheres Bargaining and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 988-1010, December.
    2. Mortensen, Dale & Pissarides, Christopher, 2011. "Job Creation and Job Destruction in the Theory of Unemployment," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 1-19.
    3. repec:syd:wpaper:2123/9993 is not listed on IDEAS
    4. Daijiro Okada & Olivier Tercieux, 2012. "Log-linear dynamics and local potential," PSE-Ecole d'économie de Paris (Postprint) halshs-00754591, HAL.
    5. Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
    6. Sandholm, William H. & Staudigl, Mathias, 2016. "Large Deviations and Stochastic Stability in the Small Noise Double Limit, I: Theory," Center for Mathematical Economics Working Papers 505, Center for Mathematical Economics, Bielefeld University.
    7. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    8. Mortensen, Dale T. & Pissarides, Christopher A., 1999. "New developments in models of search in the labor market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 39, pages 2567-2627, Elsevier.
    9. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.
    10. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    11. Okada, Daijiro & Tercieux, Olivier, 2012. "Log-linear dynamics and local potential," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1140-1164.
    12. Sandholm, William H. & Staudigl, Mathias, 2016. "Large Deviations and Stochastic Stability in the Small Noise Double Limit, II: The Logit Model," Center for Mathematical Economics Working Papers 506, Center for Mathematical Economics, Bielefeld University.
    13. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    14. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    15. Sandholm, William H. & Staudigl, Mathias, 2016. "Large deviations and stochastic stability in the small noise double limit," Theoretical Economics, Econometric Society, vol. 11(1), January.
    16. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    17. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 381-389, May.
    18. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    19. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    20. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    21. Manser, Marilyn & Brown, Murray, 1980. "Marriage and Household Decision-Making: A Bargaining Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 31-44, February.
    22. Marianna Belloc & Samuel Bowles, 2013. "The Persistence of Inferior Cultural-Institutional Conventions," American Economic Review, American Economic Association, vol. 103(3), pages 93-98, May.
    23. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    24. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    25. repec:hal:pseose:halshs-00754591 is not listed on IDEAS
    26. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
    27. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    28. Naidu, Suresh & Hwang, Sung-Ha & Bowles, Samuel, 2010. "Evolutionary bargaining with intentional idiosyncratic play," Economics Letters, Elsevier, vol. 109(1), pages 31-33, October.
    29. Dindos, Martin & Mezzetti, Claudio, 2006. "Better-reply dynamics and global convergence to Nash equilibrium in aggregative games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 261-292, February.
    30. H. Peyton Young, 1998. "Conventional Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(4), pages 773-792.
    31. Peter A. Diamond, 1982. "Wage Determination and Efficiency in Search Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 217-227.
    32. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    33. McElroy, Marjorie B & Horney, Mary Jean, 1981. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 333-349, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    as


    Cited by:

    1. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.
    2. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    3. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    4. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    5. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    6. Bilancini, Ennio & Boncinelli, Leonardo & Vicario, Eugenio, 2024. "Memory retrieval in the demand game with a few possible splits: Unfair conventions emerge in fair settings," Journal of Economic Dynamics and Control, Elsevier, vol. 165(C).
    7. Abhimanyu Khan, 2021. "Evolution of conventions in games between behavioural rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 209-224, October.
    8. Ennio Bilancini & Leonardo Boncinelli, 2018. "Social coordination with locally observable types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 975-1009, June.
    9. Arigapudi, Srinivas, 2020. "Exit from equilibrium in coordination games under probit choice," Games and Economic Behavior, Elsevier, vol. 122(C), pages 168-202.
    10. Arigapudi, Srinivas, 2024. "Transitions between equilibria in Bilingual Games under Probit Choice," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    11. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    12. Sawa, Ryoji & Wu, Jiabin, 2018. "Reference-dependent preferences, super-dominance and stochastic stability," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 96-104.
    13. Sawa, Ryoji & Wu, Jiabin, 2018. "Prospect dynamics and loss dominance," Games and Economic Behavior, Elsevier, vol. 112(C), pages 98-124.
    14. Chongyi Zhong & Hui Yang & Zixin Liu & Juanyong Wu, 2020. "Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    15. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.

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    More about this item

    Keywords

    Evolution; Coordination; Logit; Payoff dependence;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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