IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v89y2019i2d10.1007_s00186-018-0644-2.html
   My bibliography  Save this article

New results on the existence of open loop Nash equilibria in discrete time dynamic games via generalized Nash games

Author

Listed:
  • Mathew P. Abraham

    (Indian Institute of Technology Bombay)

  • Ankur A. Kulkarni

    (Indian Institute of Technology Bombay)

Abstract

We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). A classical approach to DTDGs involves analyzing the problem using optimal control theory. Sufficient conditions for the existence of open-loop Nash equilibria obtained from this approach are mainly limited to linear-quadratic games (Başar and Olsder in Dynamic noncooperative game theory, 2nd edn, SIAM, Philadelphia, 1999). Another approach of analysis is to substitute the dynamics and transform the game into a static game. But the substitution of state dynamics makes the objective functions of the resulting static problems extremely hard to analyze. We introduce a third approach in which the dynamics are not substituted, but retained as constraints in the optimization problem of each player, resulting thereby in a generalized Nash game. Using this, we give sufficient conditions for the existence of open-loop Nash equilibria for a class of DTDGs where the cost functions of players admit a quasi-potential function. Our results apply with nonlinear dynamics and without stage additive cost functions, and allow constraints on state and actions spaces, and in some cases, yield a generalization of similar results from linear-quadratic games.

Suggested Citation

  • Mathew P. Abraham & Ankur A. Kulkarni, 2019. "New results on the existence of open loop Nash equilibria in discrete time dynamic games via generalized Nash games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 157-172, April.
  • Handle: RePEc:spr:mathme:v:89:y:2019:i:2:d:10.1007_s00186-018-0644-2
    DOI: 10.1007/s00186-018-0644-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-018-0644-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00186-018-0644-2?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. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    2. Agnieszka Wiszniewska-Matyszkiel, 2017. "Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 984-1007, March.
    3. Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    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. Mathew P. Abraham & Ankur A. Kulkarni, 2020. "Price-coupling games and the generation expansion planning problem," Annals of Operations Research, Springer, vol. 295(1), pages 1-19, December.

    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. Katarzyna Kańska & Agnieszka Wiszniewska-Matyszkiel, 2022. "Dynamic Stackelberg duopoly with sticky prices and a myopic follower," Operational Research, Springer, vol. 22(4), pages 4221-4252, September.
    2. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    3. Agnieszka Wiszniewska-Matyszkiel & Rajani Singh, 2020. "When Inaccuracies in Value Functions Do Not Propagate on Optima and Equilibria," Mathematics, MDPI, vol. 8(7), pages 1-25, July.
    4. Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    5. Gaballo, Gaetano & Marimon, Ramon, 2021. "Breaking the spell with credit-easing: Self-confirming credit crises in competitive search economies," Journal of Monetary Economics, Elsevier, vol. 119(C), pages 1-20.
    6. Gamba, Astrid & Regner, Tobias, 2019. "Preferences-dependent learning in the centipede game: The persistence of mistrust," European Economic Review, Elsevier, vol. 120(C).
    7. Aurélien Baillon & Zhenxing Huang & Asli Selim & Peter P. Wakker, 2018. "Measuring Ambiguity Attitudes for All (Natural) Events," Econometrica, Econometric Society, vol. 86(5), pages 1839-1858, September.
    8. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    9. Battigalli, Pierpaolo & Generoso, Nicolò, 2024. "Information flows and memory in games," Games and Economic Behavior, Elsevier, vol. 145(C), pages 356-376.
    10. Battigalli, P. & Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2016. "Analysis of information feedback and selfconfirming equilibrium," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 40-51.
    11. Sebastiano Della Lena & Fabrizio Panebianco, 2019. "Cultural Transmission with Incomplete Information: Parental Perceived Efficacy and Group Misrepresentation," Working Papers 2019:11, Department of Economics, University of Venice "Ca' Foscari".
    12. Battigalli, Pierpaolo & Panebianco, Fabrizio & Pin, Paolo, 2023. "Learning and selfconfirming equilibria in network games," Journal of Economic Theory, Elsevier, vol. 212(C).
    13. Frédéric Koessler & Marieke Pahlke, 2023. "Feedback Design in Strategic-Form Games with Ambiguity Averse Players," PSE Working Papers halshs-04039083, HAL.
    14. Simon Quemin, 2016. "Intertemporal abatement decisions under ambiguity aversion in a cap and trade," Working Papers 1604, Chaire Economie du climat.
    15. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Thomas Sargent, 2016. "A Framework for the Analysis of Self-Confirming Policies," Working Papers 573, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    16. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    17. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.
    18. Sanghyun Park & Phanish Puranam, 2020. "Learning what they think vs. learning what they do: The micro-foundations of vicarious learning," Papers 2007.15264, arXiv.org, revised Jul 2020.
    19. Stergios Athanasoglou & Valentina Bosetti & Laurent Drouet, 2017. "A Simple Framework for Climate-Change Policy under Model Uncertainty," Working Papers 2017.13, Fondazione Eni Enrico Mattei.
    20. Chen Li & Uyanga Turmunkh & Peter P. Wakker, 2019. "Trust as a decision under ambiguity," Experimental Economics, Springer;Economic Science Association, vol. 22(1), pages 51-75, March.

    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:spr:mathme:v:89:y:2019:i:2:d:10.1007_s00186-018-0644-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.