A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport - Grimm, Veronika; Hintermüller, Michael; Huber, Oliver; Schewe, Lars; Schmidt, Martin; Zöttl, Gregor (2021)
We analyze Generalized Nash Equilibrium Problems (GNEPs) for which the objectives of the individuals are interdependent and shared constraints are governed by a system of partial differential equations (PDEs). This allows us to model the strategic interaction of competing firms, which explicitly take into account the dynamics of transporting a commodity, such as natural gas, through a network. We establish existence of a variational equilibrium, which solves the considered GNEP. We identify a reformulation of the original equilibrium problem that is suited to derive and establish a solution algorithm. Based on the solutions for a test instance, we finally illustrate how our results can be used to analyze dynamic aspects such as linepack in the context of liberalized gas market