IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v33y2009i8p1593-1603.html
   My bibliography  Save this article

Single-leader-multiple-follower games with boundedly rational agents

Author

Listed:
  • Tharakunnel, Kurian
  • Bhattacharyya, Siddhartha

Abstract

This paper studies a class of hierarchical games called single-leader-multiple-follower games (SLMFGs) that have important applications in economics and engineering. We consider such games in the context of boundedly rational agents that are limited in the information and computational power they may possess. Agents in our SLMFG are modeled as adaptive learners that use simple reinforcement learning schemes to learn their optimal behavior. The proposed learning approach is illustrated using a well-studied problem in economics. It is shown that with a patiently learning leader the repeated plays of the game result in approximate equilibrium outcomes.

Suggested Citation

  • Tharakunnel, Kurian & Bhattacharyya, Siddhartha, 2009. "Single-leader-multiple-follower games with boundedly rational agents," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1593-1603, August.
    • Handle: RePEc:eee:dyncon:v:33:y:2009:i:8:p:1593-1603
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(09)00046-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    3. Rudolf Vetschera, 2003. "Experimentation and Learning in Repeated Cooperation," Computational and Mathematical Organization Theory, Springer, vol. 9(1), pages 37-60, May.
    4. Kalai, Ehud & Ledyard, John O., 1998. "Repeated Implementation," Journal of Economic Theory, Elsevier, vol. 83(2), pages 308-317, December.
    5. Kutschinski, Erich & Uthmann, Thomas & Polani, Daniel, 2003. "Learning competitive pricing strategies by multi-agent reinforcement learning," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2207-2218.
    6. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    7. 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.
    8. Radner, Roy, 1985. "Repeated Principal-Agent Games with Discounting," Econometrica, Econometric Society, vol. 53(5), pages 1173-1198, September.
    9. Kutschinski, Erich & Uthmann, Thomas & Polani, Daniel, 2003. "Learning competitive pricing strategies by multi-agent reinforcement learning," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 2207-2218, September.
    10. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    11. Vallee, Thomas & Basar, Tamer, 1999. "Off-Line Computation of Stackelberg Solutions with the Genetic Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 13(3), pages 201-209, June.
    12. Waltman, Ludo & Kaymak, Uzay, 2008. "Q-learning agents in a Cournot oligopoly model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3275-3293, October.
    13. Alemdar, Nedim M. & Sirakaya, Sibel, 2003. "On-line computation of Stackelberg equilibria with synchronous parallel genetic algorithms," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1503-1515, June.
    14. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    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. Junyi Xu, 2021. "Reinforcement Learning in a Cournot Oligopoly Model," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1001-1024, December.
    2. Grigory Belyavsky & Natalya Danilova & Guennady Ougolnitsky, 2018. "A Markovian Mechanism of Proportional Resource Allocation in the Incentive Model as a Dynamic Stochastic Inverse Stackelberg Game," Mathematics, MDPI, vol. 6(8), pages 1-10, July.

    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. Hanaki, Nobuyuki & Ishikawa, Ryuichiro & Akiyama, Eizo, 2009. "Learning games," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1739-1756, October.
    2. Mauersberger, Felix, 2019. "Thompson Sampling: Endogenously Random Behavior in Games and Markets," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203600, Verein für Socialpolitik / German Economic Association.
    3. Waltman, Ludo & Kaymak, Uzay, 2008. "Q-learning agents in a Cournot oligopoly model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3275-3293, October.
    4. Pangallo, Marco & Sanders, James B.T. & Galla, Tobias & Farmer, J. Doyne, 2022. "Towards a taxonomy of learning dynamics in 2 × 2 games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 1-21.
    5. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011, Elsevier.
    6. Sonnemans, Joep & Hommes, Cars & Tuinstra, Jan & van de Velden, Henk, 2004. "The instability of a heterogeneous cobweb economy: a strategy experiment on expectation formation," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 453-481, August.
    7. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    8. Mele, Antonio & Molnár, Krisztina & Santoro, Sergio, 2020. "On the perils of stabilizing prices when agents are learning," Journal of Monetary Economics, Elsevier, vol. 115(C), pages 339-353.
    9. Anufriev, Mikhail & Kopányi, Dávid & Tuinstra, Jan, 2013. "Learning cycles in Bertrand competition with differentiated commodities and competing learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2562-2581.
    10. De Grauwe, Paul & Markiewicz, Agnieszka, 2013. "Learning to forecast the exchange rate: Two competing approaches," Journal of International Money and Finance, Elsevier, vol. 32(C), pages 42-76.
    11. Adriaan R. Soetevent, 2006. "Empirics of the Identification of Social Interactions; An Evaluation of the Approaches and Their Results," Journal of Economic Surveys, Wiley Blackwell, vol. 20(2), pages 193-228, April.
    12. Michele Berardi, 2021. "Discrete beliefs space and equilibrium: a cautionary note," Journal of Evolutionary Economics, Springer, vol. 31(2), pages 505-532, April.
    13. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    14. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    15. Michele Berardi, 2011. "Heterogeneous sunspots solutions under learning and replicator dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 160, Economics, The University of Manchester.
    16. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    17. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    18. Michele Berardi, 2015. "Expectations formation under adaptive learning and evolutionary dynamics," Centre for Growth and Business Cycle Research Discussion Paper Series 206, Economics, The University of Manchester.
    19. Berardi, Michele, 2015. "On the fragility of sunspot equilibria under learning and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 251-265.
    20. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.

    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:dyncon:v:33:y:2009:i:8:p:1593-1603. 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.elsevier.com/locate/jedc .

    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.