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A Local Variation Method for Bilevel Nash Equilibrium Problems

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Abstract

We address the numerical approximation of bilevel problems consisting of one Nash equilibrium problem in the upper level and another Nash equilibrium problem in the lower level. These problems, widely employed in engineering and economic applications, are a generalization of the well-known Stackelberg (or bilevel optimization) problem. In this paper, we define a numerical method for bilevel Nash equilibrium problems where in the lower level there is a ratio-bounded game (introduced in Caruso, Ceparano, Morgan [CSEF Working Papers, 593 (2020)]) and in the upper level there is a potential game (introduced in Monderer, Shapley [Games Econ. Behav., 14 (1996)]). The method, relying on a derivative-free unconstrained optimization technique called local variation method, is shown to globally converge towards a solution of the problem and also allows to obtain error estimations.

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  • Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2021. "A Local Variation Method for Bilevel Nash Equilibrium Problems," CSEF Working Papers 620, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  • Handle: RePEc:sef:csefwp:620
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    References listed on IDEAS

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    1. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    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. Branzei, Rodica & Mallozzi, Lina & Tijs, Stef, 2003. "Supermodular games and potential games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 39-49, February.
    4. Shenglong Zhou & Alain B. Zemkoho & Andrey Tin, 2020. "BOLIB: Bilevel Optimization LIBrary of Test Problems," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 563-580, Springer.
    5. Elisabetta Allevi & Didier Aussel & Rossana Riccardi, 2018. "On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity," Journal of Global Optimization, Springer, vol. 70(2), pages 329-346, February.
    6. Pal, Debashis, 1991. "Cournot duopoly with two production periods and cost differentials," Journal of Economic Theory, Elsevier, vol. 55(2), pages 441-448, December.
    7. Damien J. A. Bazin, 2011. "Marketstructure and equilibrium," Post-Print halshs-00727586, HAL.
    8. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    9. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
    10. Heinrich von Stackelberg, 2011. "Market Structure and Equilibrium," Springer Books, Springer, number 978-3-642-12586-7, September.
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