We consider a class of Nash games with nonconvex coupling constraints where we leverage the theory of tangent cones to define a novel notion of local equilibrium: Clarke’s local generalized Nash equilibrium (CL-GNE).

Our first technical contribution is to show the stability of these equilibria on a specific local subset of the original feasible set.

As a second contribution, we show that the proposed notion of local equilibrium can be equivalently formulated as the solution of a quasi-variational inequality, remarkably, with equal Lagrange multipliers.

Next, we define conditions for the existence and uniqueness of the CL-GNE.

To compute such an equilibrium, we propose two discrete-time distributed dynamics, or fixed-point iterations.

Our third technical contribution is to  prove convergence under (strongly) monotone assumptions on the pseudo-gradient mapping of the game.

Finally, we apply our theoretical results to a competitive version of the optimal power flow control problem.

Paper submitted for publication in IEEE Transactions on Automatic Control – http://ieeecss.org/publication/transactions-automatic-control