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

Presented by: 
Michael Hintermüller Weierstraß-Institut für Angewandte Analysis und Stochastik, Humboldt-Universität zu Berlin
Thursday 21st March 2019 - 16:30 to 17:15
INI Seminar Room 1
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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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons