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

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  • Francesco Caruso

    (University of Naples Federico II)

  • Maria Carmela Ceparano

    (University of Naples Federico II)

  • Jacqueline Morgan

    (University of Naples Federico II)

Abstract

In one-leader one-follower two-stage games, also called Stackelberg games, multiplicity of subgame perfect Nash equilibria (henceforth SPNEs) 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, 2019. "Subgame Perfect Nash Equilibrium: A Learning Approach via Costs to Move," Dynamic Games and Applications, Springer, vol. 9(2), pages 416-432, June.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0277-3
    DOI: 10.1007/s13235-018-0277-3
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    References listed on IDEAS

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    1. 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.
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    4. 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.
    5. 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.
    6. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01337293, HAL.
    7. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    8. G. De Marco & J. Morgan, 2008. "Slightly Altruistic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 347-362, May.
    9. 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.
    10. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.
    11. 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.
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    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.

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