Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players
Year: 2018
Type: preprint
Abstract: After defining a pure-action profile in a nonatomic aggregative game, where players have specific compact convex pure-action sets and nonsmooth convex cost functions, as a square-integrable function, we characterize a Wardrop equilibrium as a solution to an infinite-dimensional generalized variational inequality. We show the existence of Wardrop equilibrium and variational Wardrop equilibrium, a concept of equilibrium adapted to the presence of coupling constraints, in monotone nonatomic aggregative games. The uniqueness of (variational) Wardrop equilibrium is proved for strictly or aggregatively strictly monotone nonatomic aggregative games. We then show that, for a sequence of finite-player aggregative games with aggregative constraints, if the players' pure-action sets converge to those of a strongly (resp. aggregatively strongly) monotone nonatomic aggregative game, and the aggregative constraints in the finite-player games converge to the aggregative constraint of the nonatomic game, then a sequence of so-called variational Nash equilibria in these finite-player games converge to the variational Wardrop equilibrium in pure-action profile (resp. aggregate-action profile). In particular, it allows the construction of an auxiliary sequence of games with finite-dimensional equilibria to approximate the infinite-dimensional equilibrium in such a nonatomic game. Finally, we show how to construct auxiliary finite-player games for two general classes of nonatomic games.
Source: arXiv (Cornell University)
Authors: Jacquot, Paulin, Wan, Cheng
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, École Polytechnique, Centre de Mathématiques Appliquées de l'École polytechnique, Centre Inria de Saclay, Électricité de France (France), TROPICAL: Méthodes tropicales: structures, algorithmes et interactions, Institut de Mathématiques de Jussieu-Paris Rive Gauche
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2807916009