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An Enhanced Gradient Algorithm for Computing Generalized Nash Equilibrium Applied to Electricity Market Games

Author

Listed:
  • Adriano C. Lisboa

    (Gaia, Belo Horizonte 31310-260, MG, Brazil
    ENACOM, Belo Horizonte 31275-100, MG, Brazil
    Electrical Engineering Department, Federal University of Minas Gerais, Belo Horizonte 31270-901, MG, Brazil
    Gratuated Program on Computational and Mathematical Modelling, Federal Center of Technological Education of Minas Gerais, Belo Horizonte 30421-169, MG, Brazil)

  • Fellipe F. G. Santos

    (Companhia Energética de Minas Gerais S.A., Belo Horizonte 30190-131, MG, Brazil)

  • Douglas A. G. Vieira

    (ENACOM, Belo Horizonte 31275-100, MG, Brazil
    Gratuated Program on Computational and Mathematical Modelling, Federal Center of Technological Education of Minas Gerais, Belo Horizonte 30421-169, MG, Brazil)

  • Rodney R. Saldanha

    (Electrical Engineering Department, Federal University of Minas Gerais, Belo Horizonte 31270-901, MG, Brazil)

  • Felipe A. C. Pereira

    (ENACOM, Belo Horizonte 31275-100, MG, Brazil)

Abstract

This paper introduces an enhanced algorithm for computing generalized Nash equilibria for multiple player nonlinear games, which degenerates in a gradient algorithm for single player games (i.e., optimization problems) or potential games (i.e., equivalent to minimizing the respective potential function), based on the Rosen gradient algorithm. Analytical examples show that it has similar theoretical guarantees of finding a generalized Nash equilibrium when compared to the relaxation algorithm, while numerical examples show that it is faster. Furthermore, the proposed algorithm is as fast as, but more stable than, the Rosen gradient algorithm, especially when dealing with constraints and non-convex games. The algorithm is applied to an electricity market game representing the current electricity market model in Brazil.

Suggested Citation

  • Adriano C. Lisboa & Fellipe F. G. Santos & Douglas A. G. Vieira & Rodney R. Saldanha & Felipe A. C. Pereira, 2025. "An Enhanced Gradient Algorithm for Computing Generalized Nash Equilibrium Applied to Electricity Market Games," Energies, MDPI, vol. 18(3), pages 1-14, February.
    • Handle: RePEc:gam:jeners:v:18:y:2025:i:3:p:727-:d:1583922
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    References listed on IDEAS

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    4. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    5. Dindos, Martin & Mezzetti, Claudio, 2006. "Better-reply dynamics and global convergence to Nash equilibrium in aggregative games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 261-292, February.
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