A constrained optimization reformulation of the generalized Nash equilibrium problem

Abstract

The generalized Nash equilibrium problem is an extension of the Nash equilibrium problem by assuming that each player’s feasible set depends on the rival player’s strategies. By the Nikaido-Isoda function, we reformulate the generalized Nash equilibrium problem as a constrained optimization problem. This reformulation allows us to apply optimization techniques to the constrained optimization problem in order to solve the generalized Nash equilibrium problem. Conditions for the stationary point to be the global minimum of the constrained optimization problem are also given.

Keywords:

• Generalized Nash equilibrium problem
• Nikaido-Isoda function
• constrained optimization problem
• Stationary point