In this talk we introduce the audience to the concept of generalized Nash games; these are a class of Nash games introduced in the 50's, currently undergoing a sustained interest from the mathematics and engineering communities, due to advances in possible solution techniques, as well as their potential for applications.
We therefore will focus our talk in two directions: one more theoretical, where we introduce a parametrization technique 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 then move into the second direction, where we give many illustrative examples of how our computational technique is used to compute the solution sets of known generalized Nash games previously not solved by other existing techniques. We close with the presentation of two very different applied problems formulated as a generalized Nash game: a model of an environmental accord between countries sharing geographic proximity, and another model of several HIV+ and HIV- individuals engaged in casual encounters which may lead to the spread of HIV. We highlight the possible advantages of modeling these problems as generalized Nash games, as well as the diversity of applications that could be targeted with this modelling framework.