A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem

•We studied a shared constrained approximation of the generalized Nash game.•The game is reformulated as a family of parametric variational inequalities.•We proposed a numerical approach to approximate the solution set of the game.•We studied and solved a game of environmental accords between countries. In this paper, we present a numerical method to describe the solution set of a generalized Nash equilibrium problem (GNEP). Previous approaches show how to reformulate the GNEP as a family of parametric variational inequalities in the special case where the game has shared constraints. We extend this result to generalized Nash problems by means of an umbrella shared constraint approximation of the game. We show the validity of our approach on numerical examples from the literature, and we provide new results that pinpoint the handling of the algorithm’s parameters for its implementation. Last but not least, we extend, solve, and discuss an applied example of a generalized Nash equilibrium problem of environmental accords between countries.