Generalized Nash Equilibrium Problems with Application to Spot Markets with Gas Transport

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• Michael Hintermüller (Weierstraß-Institut für Angewandte Analysis und Stochastik; Humboldt-Universität zu Berlin)
• Thursday 21 March 2019, 16:30-17:15
• Seminar Room 1, Newton Institute.

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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 GNE Ps and a spot-market model are developed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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