IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2302.09131.html
   My bibliography  Save this paper

Nash equilibrium selection by eigenvalue control

Author

Listed:
  • Wang Zhijian

Abstract

People choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. The process can be modelled as an evolutionary game dynamics system, which may be controllable. In modern control theory, eigenvalue (pole) assignment is a basic approach to designing a full-state feedback controller, which can influence the outcome of a game. This study shows that, in a game with two Nash equilibria, the long-running strategy distribution can be controlled by pole assignment. We illustrate a theoretical workflow to design and evaluate the controller. To our knowledge, this is the first realisation of the control of equilibrium selection by design in the game dynamics theory paradigm. We hope the controller can be verified in a laboratory human subject game experiment.

Suggested Citation

  • Wang Zhijian, 2023. "Nash equilibrium selection by eigenvalue control," Papers 2302.09131, arXiv.org.
    • Handle: RePEc:arx:papers:2302.09131
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2302.09131
    File Function: Latest version
    Download Restriction: no
    ---><---

    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, April.
    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. Bin Xu & Shuang Wang & Zhijian Wang, 2014. "Periodic frequencies of the cycles in 2 × 2 games: evidence from experimental economics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(2), pages 1-10, February.
    4. David Avis & Gabriel Rosenberg & Rahul Savani & Bernhard Stengel, 2010. "Enumeration of Nash equilibria for two-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 9-37, January.
    5. Zhijian Wang & Shujie Zhou & Qinmei Yao & Yijia Wang, 2022. "Dynamic Structure in Four-strategy Game: Theory and Experiment," Papers 2203.14669, arXiv.org.
    6. Larry Samuelson, 2016. "Game Theory in Economics and Beyond," Journal of Economic Perspectives, American Economic Association, vol. 30(4), pages 107-130, Fall.
    7. Wang Zhijian, 2022. "Game Dynamics Structure Control by Design: an Example from Experimental Economics," Papers 2203.06088, arXiv.org.
    8. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151.
    9. Wang, Yijia & Chen, Xiaojie & Wang, Zhijian, 2017. "Testability of evolutionary game dynamics based on experimental economics data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 455-464.
    10. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    11. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, April.
    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. Wang Zhijian & Shan Lixia & Yao Qinmei & Wang Yijia, 2024. "Human game experiment to verify the equilibrium selection controlled by design," Papers 2411.06847, arXiv.org.

    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. Wang Yijia & Wang Zhijian, 2023. "Pulse in collapse: a game dynamics experiment," Papers 2302.09336, arXiv.org.
    2. Wang Zhijian, 2022. "Game Dynamics Structure Control by Design: an Example from Experimental Economics," Papers 2203.06088, arXiv.org.
    3. Zhijian Wang & Shujie Zhou & Qinmei Yao & Yijia Wang, 2022. "Dynamic Structure in Four-strategy Game: Theory and Experiment," Papers 2203.14669, arXiv.org.
    4. Wang Zhijian & Shan Lixia & Yao Qinmei & Wang Yijia, 2024. "Human game experiment to verify the equilibrium selection controlled by design," Papers 2411.06847, arXiv.org.
    5. Zhijian Wang & Qinmei Yao & Yijia Wang, 2022. "Eigen mode selection in human subject game experiment," Papers 2204.08071, arXiv.org.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    7. Hadi Charkhgard & Martin Savelsbergh & Masoud Talebian, 2018. "Nondominated Nash points: application of biobjective mixed integer programming," 4OR, Springer, vol. 16(2), pages 151-171, June.
    8. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    9. Zhijian Wang & Bin Xu, 2014. "Cycling in stochastic general equilibrium," Papers 1410.8432, arXiv.org.
    10. 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.
    11. Rahul Savani & Bernhard Stengel, 2015. "Game Theory Explorer: software for the applied game theorist," Computational Management Science, Springer, vol. 12(1), pages 5-33, January.
    12. Dirk Helbing & Anders Johansson, 2010. "Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-15, October.
    13. Arigapudi, Srinivas, 2024. "Evolutionary dynamics in bilingual games," Journal of Economic Dynamics and Control, Elsevier, vol. 165(C).
    14. 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.
    15. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    16. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    17. 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).
    18. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    19. Wang, Yijia & Chen, Xiaojie & Wang, Zhijian, 2017. "Testability of evolutionary game dynamics based on experimental economics data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 455-464.
    20. Nathalie Greenan & Marc-Arthur Diaye & Patricia Crifo, 2004. "Pourquoi les entreprises évaluent-elles individuellement leurs salariés ?," Économie et Prévision, Programme National Persée, vol. 164(3), pages 27-55.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2302.09131. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.