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Nash equilibrium selection by eigenvalue control

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  • 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.

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

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    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.
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    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, December.
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    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.

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