2015-09-17Zeitschriftenartikel DOI: 10.1137/14096829X
Generalized Nash Equilibrium Problems inBanach Spaces: Theory, Nikaido–Isoda-Based Path-Following Methods, and Applications
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät
Building upon the results in [M. Hintermüller and T. Surowiec, Pac. J. Optim., 9 (2013), pp. 251–273], a class of noncooperative Nash equilibrium problems is presented, in which the feasible set of each player is perturbed by the decisions of their competitors via a convex constraint. In addition, for every vector of decisions, a common “state” variable is given by the solution of an affine linear equation. The resulting problem is therefore a generalized Nash equilibrium problem (GNEP). The existence of an equilibrium for this problem is demonstrated, and first-order optimality conditions are derived under a constraint qualification. An approximation scheme is proposed, which involves the solution of a parameter-dependent sequence of standard Nash equilibrium problems. An associated path-following strategy based on the Nikaido–Isoda function is then proposed. Function- space-based numerics for parabolic GNEPs and a spot-market model are developed.
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