A Homotopy Method for Equilibrium Programming under Uncertainty.

We consider a homotopy method for solving stochastic Nash equilibrium models. The algorithm works by following, via a predictor-corrector method, the one-dimensional manifold of the homotopy constructed to connect the systems of equations describing the solution set of the scenario equilibrium model (no nonanticipativity constraints) and the stochastic equilibrium model. The predictor and corrector phases of this homotopy method require the usual solutions of large linear systems, a computationally expensive task, which we render less difficult through our use of Jacobi techniques designed to take advantage of the problem's near separability across scenarios.