On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball

In this paper we propose an exact, deterministic, and fully continuous reformulation of generalized Nash games characterized by the presence of soft coupling constraints in the form of distributionally robust (DR) joint chance-constraints (CCs). We first rewrite the underlying uncertain game introducing mixed-integer variables to cope with DR-CCs, where the integer restriction actually amounts to a binary decision vector only, and then extend it to an equivalent deterministic problem with one additional agent handling all those introduced variables. Successively we show that, by means of a careful choice of tailored penalty functions, the extended deterministic game with additional agent can be equivalently recast in a fully continuous setting.