IDEAS home Printed from https://ideas.repec.org/p/sef/csefwp/476.html
   My bibliography  Save this paper

Subgame Perfect Nash Equilibrium: A Learning Approach Via Costs to Move

Author

Listed:

Abstract

In one-leader one-follower two-stage games, also called Stackelberg games, multiplicity of Subgame Perfect Nash Equilibria (henceforth SPNE) arises when the best reply correspondence of the follower is not a single-valued map. This paper concerns a new method to approach SPNEs which makes use of a sequence of SPNEs of perturbed games where the best reply correspondence of the follower is single-valued. The sequence is generated by a learning method where the payoff functions of both players are modified subtracting a term that represents a physical and behavioral cost to move and which relies on the proximal point methods linked to the Moreau-Yosida regularization. Existence results of SPNEs approached via this method are provided under mild assumptions on the data, together with numerical examples and connections with other methods to construct SPNEs.

Suggested Citation

  • Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Subgame Perfect Nash Equilibrium: A Learning Approach Via Costs to Move," CSEF Working Papers 476, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 20 Jul 2018.
  • Handle: RePEc:sef:csefwp:476
    Note: This paper was previously circulated with the title “Proximal Approach in Selection of Subgame Perfect Nash Equilibria”
    as

    Download full text from publisher

    File URL: http://www.csef.it/WP/wp476.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01337293, HAL.
    2. Ceparano, Maria Carmela & Quartieri, Federico, 2017. "Nash equilibrium uniqueness in nice games with isotone best replies," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 154-165.
    3. M. Beatrice Lignola & Jacqueline Morgan, 2017. "Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 183-202, April.
    4. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Games and Dynamic Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8442, February.
    5. M. Beatrice Lignola & Jacqueline Morgan, 2014. "Viscosity Solutions for Bilevel Problems with Nash Equilibrium Constraints," CSEF Working Papers 367, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 02 Oct 2014.
    6. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.
    7. G. De Marco & J. Morgan, 2008. "Slightly Altruistic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 347-362, May.
    8. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games," CSEF Working Papers 471, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 18 Jun 2017.
    9. M. B. Lignola & J. Morgan, 1997. "Stability of Regularized Bilevel Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 575-596, June.
    10. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    11. M. Kojima & A. Okada & S. Shindoh, 1985. "Strongly Stable Equilibrium Points of N -Person Noncooperative Games," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 650-663, November.
    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. Francesco Caruso & M. Beatrice Lignola & Jacqueline Morgan, 2020. "Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 77-138, Springer.
    2. Sjur Didrik Flåm, 2021. "Games and cost of change," Annals of Operations Research, Springer, vol. 301(1), pages 107-119, June.
    3. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2022. "Asymptotic Behavior of Subgame Perfect Nash Equilibria in Stackelberg Games," CSEF Working Papers 661, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

    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. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2022. "Asymptotic Behavior of Subgame Perfect Nash Equilibria in Stackelberg Games," CSEF Working Papers 661, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Francesco Caruso & M. Beatrice Lignola & Jacqueline Morgan, 2020. "Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 77-138, Springer.
    3. M. Beatrice Lignola & Jacqueline Morgan, 2012. "Approximating Security Values of MinSup Problems with Quasi-variational Inequality Constraints," CSEF Working Papers 321, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 09 Oct 2014.
    4. Gaoxi Li & Zhongping Wan, 2018. "On Bilevel Programs with a Convex Lower-Level Problem Violating Slater’s Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 820-837, December.
    5. M. Beatrice Lignola & Jacqueline Morgan, 2013. "Asymptotic Behavior of Regularized OptimizationProblems with Quasi-variational Inequality Constraints," CSEF Working Papers 350, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Henri Bonnel & Léonard Todjihoundé & Constantin Udrişte, 2015. "Semivectorial Bilevel Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 464-486, November.
    7. Bich, Philippe, 2019. "Strategic uncertainty and equilibrium selection in discontinuous games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 786-822.
    8. Gaoxi Li & Xinmin Yang, 2021. "Convexification Method for Bilevel Programs with a Nonconvex Follower’s Problem," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 724-743, March.
    9. M. Lignola & Jacqueline Morgan, 2012. "Approximate values for mathematical programs with variational inequality constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 485-503, October.
    10. Lorenzo Lampariello & Simone Sagratella, 2020. "Numerically tractable optimistic bilevel problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 277-303, June.
    11. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    12. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    13. M. Beatrice Lignola & Jacqueline Morgan, 2015. "MinSup Problems with Quasi-equilibrium Constraints and Viscosity Solutions," CSEF Working Papers 393, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    14. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    15. 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.
    16. Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Veronica Piccialli, 2016. "A Game-Theoretic Approach for Regulating Hazmat Transportation," Transportation Science, INFORMS, vol. 50(2), pages 424-438, May.
    17. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    18. Cerulli, Martina & Serra, Domenico & Sorgente, Carmine & Archetti, Claudia & Ljubić, Ivana, 2023. "Mathematical programming formulations for the Collapsed k-Core Problem," European Journal of Operational Research, Elsevier, vol. 311(1), pages 56-72.
    19. Anna Castañer & Jesús Marín-Solano & Carmen Ribas, 2021. "A time consistent dynamic bargaining procedure in differential games with hterogeneous discounting," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 555-584, June.
    20. Chan Y. Han & Brian J. Lunday & Matthew J. Robbins, 2016. "A Game Theoretic Model for the Optimal Location of Integrated Air Defense System Missile Batteries," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 405-416, August.

    More about this item

    Keywords

    Non-cooperative game; Stackelberg game; subgame perfect Nash equilibrium; selection; learning method; cost to move; proximal point method.;
    All these keywords.

    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:sef:csefwp:476. 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: Dr. Maria Carannante (email available below). General contact details of provider: https://edirc.repec.org/data/cssalit.html .

    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.