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

Adriano C. Lisboa (), Fellipe F. G. Santos, Douglas A. G. Vieira, Rodney R. Saldanha and Felipe A. C. Pereira
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Adriano C. Lisboa: Gaia, Belo Horizonte 31310-260, 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
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

Energies, 2025, vol. 18, issue 3, 1-14

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.

Keywords: Brazilian electricity market; Rosen algorithm; generalized Nash equilibrium (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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