Groupe d’études et de recherche en analyse des décisions

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

Monica Cojocaru University of Guelph, Canada

In this talk we introduce a parametrization technique that leads to the use of 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, based on these, we introduce a computational method that practitioners can implement in applied problems modeled as generalized Nash games with shared constraints, as long as the applied problems are satisfying several assumptions present in the current optimization literature.

We give many illustrative examples of how our computational technique is used to compute the solution sets of know generalized Nash games previously not solved by other existing techniques. We close with the presentation of an applied problem formulated as a generalized Nash game, namely a model of an environmental accord between countries. We highlight the advantages of modeling this problem within a generalized Nash game framework.

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