Risk-neutral PDE-constrained generalized Nash equilibrium problems

Abstract A class of risk-neutral generalized Nash equilibrium problems is introduced in which the feasible strategy set each player subject to a common linear elliptic partial differential equation with random inputs. In addition, player’s actions are taken from bounded, closed, and convex on individual strategies bound constraint state variable. Existence equilibria first-order optimality conditions derived by exploiting higher integrability regularity field variables specially tailored qualification for GNEPs assumed structure. relaxation scheme based Moreau-Yosida approximation proposed, ultimately leads numerical algorithms as well GNEP whole. The related probability constraints viability proposed demonstrated via several examples.