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

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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.

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  • 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”
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    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, 2024. "Asymptotic behavior of subgame perfect Nash equilibria in Stackelberg games," Annals of Operations Research, Springer, vol. 336(3), pages 1573-1590, May.
    4. Bae, Sang Hoo & Zhu, Qingyun & Sarkis, Joseph, 2024. "Supply chain interactions and strategic product deletion Decisions: A Game-Theoretic analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).

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    Keywords

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