Ricerc@Sapienza

Objectives
Many noncooperative multi-agent systems can be modeled as generalized Nash equilibrium problems (GNEPs) with mixed-integer strategy sets, i.e., games in which the players have integrality constraints. Nevertheless in the literature there is a lack of general algorithms to compute solutions of mixed-integer GNEPs. We develop new enumerative and best-response solution methods for mixed-integer GNEPs, and we apply them to compute equilibria of noncooperative games from machine learning and transportation problems.

Methodology
The enumerative solution methods we consider include both branch-and-bound methods based on merit functions for the mixed-integer GNEP, and branch-and-prune ones that exploit the concept of dominance to make effective cuts. Moreover, we intend to define suitable assumptions based on monotonicity and metric regularity properties in order to obtain variants of these enumerative procedures to compute the whole equilibrium set and to perform a general equilibrium selection for the game.
As a second line of research, and besides potential and 2-groups partitionable games, we want to define new classes of mixed-integer problems, namely P-upsilon games, for which player best-response methods converge to equilibria, and thus solutions exist.

Expected results
We want to develop new theoretical results in order to improve the literature on mixed-integer GNEPs.
We expect to develop new powerful enumerative and best-response algorithms for the solution of mixed-integer GNEPs. Suitable variants of these methods, such as the equilibrium selection algorithm, will be employed to tackle important applications in machine learning and transportation problems. Specifically, we intend to define and solve new generalizations of the multi-agent models stemmed from generative adversarial networks.
Moreover we want to study other fundamental applications of our games, i.e., noncooperative fixed charge transportation problems.