IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0105391.html
   My bibliography  Save this article

Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Author

Listed:
  • Qian Zhuang
  • Zengru Di
  • Jinshan Wu

Abstract

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs.

Suggested Citation

  • Qian Zhuang & Zengru Di & Jinshan Wu, 2014. "Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-16, August.
    • Handle: RePEc:plo:pone00:0105391
    DOI: 10.1371/journal.pone.0105391
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0105391
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0105391&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0105391?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Drew Fudenberg & David K. Levine, 2009. "Learning and Equilibrium," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 385-420, May.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    5. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Benndorf, Volker & Martínez-Martínez, Ismael, 2017. "Perturbed best response dynamics in a hawk–dove game," Economics Letters, Elsevier, vol. 153(C), pages 61-64.
    2. Ivan S Menshikov & Alexsandr V Shklover & Tatiana S Babkina & Mikhail G Myagkov, 2017. "From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-17, November.
    3. Lee, Joung Hun & Kakinuma, Kaoru & Okuro, Toshiya & Iwasa, Yoh, 2015. "Coupled social and ecological dynamics of herders in Mongolian rangelands," Ecological Economics, Elsevier, vol. 114(C), pages 208-217.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. van Damme, E.E.C., 2000. "Non-cooperative Games," Discussion Paper 2000-96, Tilburg University, Center for Economic Research.
    2. van Damme, E.E.C., 2015. "Game theory : Noncooperative games," Other publications TiSEM ff518f2b-501f-4d99-817b-c, Tilburg University, School of Economics and Management.
    3. Dieter Balkenborg & Rosemarie Nagel, 2016. "An Experiment on Forward vs. Backward Induction: How Fairness and Level k Reasoning Matter," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 378-408, August.
    4. Yoo, Seung Han, 2014. "Learning a population distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 188-201.
    5. Hendrik Vollmer, 2013. "What kind of game is everyday interaction?," Rationality and Society, , vol. 25(3), pages 370-404, August.
    6. Bryan McCannon, 2011. "Coordination between a sophisticated and fictitious player," Journal of Economics, Springer, vol. 102(3), pages 263-273, April.
    7. Topi Miettinen, 2012. "Paying attention to payoffs in analogy-based learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 193-222, May.
    8. Rick, Scott & Weber, Roberto A., 2010. "Meaningful learning and transfer of learning in games played repeatedly without feedback," Games and Economic Behavior, Elsevier, vol. 68(2), pages 716-730, March.
    9. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    10. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    11. Xiao Han & Yun Yu & Bin Jia & Zi‐You Gao & Rui Jiang & H. Michael Zhang, 2021. "Coordination Behavior in Mode Choice: Laboratory Study of Equilibrium Transformation and Selection," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3635-3656, October.
    12. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    13. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2007. "Partial bandwagon effects and local interactions," Games and Economic Behavior, Elsevier, vol. 61(2), pages 179-197, November.
    14. Fogale, Alberto & Pellizzari, Paolo & Warglien, Massimo, 2007. "Learning and equilibrium selection in a coordination game with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 519-527.
    15. Auriol, Emmanuelle & Platteau, Jean-Philippe & Camilotti, Giula, 2017. "Eradicating Women-Hurting Customs: What Role for Social Engineering?," CEPR Discussion Papers 12107, C.E.P.R. Discussion Papers.
    16. Jiang, Ge & Weidenholzer, Simon, 2016. "Local Interactions under Switching Costs," Economics Discussion Papers 17770, University of Essex, Department of Economics.
    17. Anke Gerbery & Thorsten Hensz & Bodo Vogtx, 2010. "Rational Investor Sentimentina Repeated Stochastic Game with Imperfect Monitoring," Post-Print hal-00911824, HAL.
    18. Ge Jiang & Simon Weidenholzer, 2017. "Local interactions under switching costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 571-588, October.
    19. Drew Fudenberg, 2006. "Advancing Beyond Advances in Behavioral Economics," Journal of Economic Literature, American Economic Association, vol. 44(3), pages 694-711, September.
    20. Kyle Hyndman & Antoine Terracol & Jonathan Vaksmann, 2009. "Learning and sophistication in coordination games," Experimental Economics, Springer;Economic Science Association, vol. 12(4), pages 450-472, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0105391. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.