Técnicas de ponto interior e direções viáveis para problemas de equilíbrio de Nash generalizado com restrições compartilhadas

Abstract

In this work we present two feasible direction and interior point methods for the computation of the normalized equilibrium of the generalized Nash equilibrium problem, GNEP. The GNEP generalizes the classical Nash equilibrium problem, NEP, in the sense that the strategy sets of each player depend on the strategies of the rival players. As in the NEP, the GNEP involves two or more players competing under the assumption that there is no collaboration between them and each player, has an associated optimization problem. Through a reformulation that concatenates the optimality conditions of each player’s optimization problem, we can obtain the normalized solution to the GNEP. The algorithms presented in this work are Newton type and solve the concatenation of the optimality conditions, using also potential functions that decrease in each iteration. Thus the algorithms generate a sequence of feasible points that converge to the normalized solution of the GNEP. The global convergence of both algorithms is tested under certain assumptions and their applicability and efficiency are shown by numerical tests.