On describing the solution sets of generalized Nash games with shared constraints

Abstract

In this paper we use parametric variational inequality problems for the purpose of describing entire solution sets of generalized Nash games with shared constraints. We prove two theoretical results and we introduce a computational method that practitioners can implement in applied problems modeled as generalized Nash games, under assumptions present in the current literature. Further, we give illustrative examples of how our computational technique is used to derive solution sets of known generalized Nash games previously not solved by existing techniques. We close with the presentation of an applied problem formulated as a generalized Nash game, namely a model of a joint implementation environmental accord between countries. We discuss the possible advantages of modeling it within a generalized Nash game framework.