IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v549y2020ics0378437120301023.html
   My bibliography  Save this article

Optimal learning dynamics of multiagent system in restless multiarmed bandit game

Author

Listed:
  • Nakayama, Kazuaki
  • Nakamura, Ryuzo
  • Hisakado, Masato
  • Mori, Shintaro

Abstract

Social learning is learning through the observation of or interaction with other individuals; it is critical in the understanding of the collective behaviors of humans in social physics. We study the learning process of agents in a restless multiarmed bandit (rMAB). The binary payoff of each arm changes randomly and agents maximize their payoffs by exploiting an arm with payoff 1, searching the arm at random (individual learning), or copying an arm exploited by other agents (social learning). The system has Pareto and Nash equilibria in the mixed strategy space of social and individual learning. We study several models in which agents maximize their expected payoffs in the strategy space, and demonstrate analytically and numerically that the system converges to the equilibria. We also conducted an experiment and investigated whether human participants adopt the optimal strategy. In this experiment, three participants play the game. If the reward of each group is proportional to the sum of the payoffs, the median of the social learning rate almost coincides with that of the Pareto equilibrium.

Suggested Citation

  • Nakayama, Kazuaki & Nakamura, Ryuzo & Hisakado, Masato & Mori, Shintaro, 2020. "Optimal learning dynamics of multiagent system in restless multiarmed bandit game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
  • Handle: RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437120301023
    DOI: 10.1016/j.physa.2020.124314
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120301023
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2020.124314?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    3. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    4. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
    5. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    6. repec:cup:cbooks:9781316779309 is not listed on IDEAS
    7. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781316624791, October.
    8. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    9. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781107172661, October.
    Full references (including those not matched with items on IDEAS)

    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. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    2. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    3. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.
    4. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    5. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    6. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    7. Sandholm, William H., 2007. "Evolution in Bayesian games II: Stability of purified equilibria," Journal of Economic Theory, Elsevier, vol. 136(1), pages 641-667, September.
    8. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.
    9. Xiaotie Deng & Xinyan Hu & Tao Lin & Weiqiang Zheng, 2021. "Nash Convergence of Mean-Based Learning Algorithms in First Price Auctions," Papers 2110.03906, arXiv.org, revised Feb 2023.
    10. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    11. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
    12. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    13. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
    14. Leslie, David S. & Perkins, Steven & Xu, Zibo, 2020. "Best-response dynamics in zero-sum stochastic games," Journal of Economic Theory, Elsevier, vol. 189(C).
    15. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    16. Stephenson, Daniel, 2019. "Coordination and evolutionary dynamics: When are evolutionary models reliable?," Games and Economic Behavior, Elsevier, vol. 113(C), pages 381-395.
    17. Emerson Melo, 2021. "Learning In Random Utility Models Via Online Decision Problems," CAEPR Working Papers 2022-003 Classification-D, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    18. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    19. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
    20. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.

    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:eee:phsmap:v:549:y:2020:i:c:s0378437120301023. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.