joint work with Maria Carmela Ceparano, Jacqueline Morgan
We propose an algorithm based on a non-standard (non-convex) relaxation of the classical best response approach which guarantees the convergence to a Nash equilibrium in two-player non zero-sum games when the best response functions are not linear, both their compositions are not contractions and the strategy sets are Hilbert spaces. First, we prove a uniqueness result for Nash equilibria. Then, we define an iterative method and a numerical approximation scheme, relying on a continuous optimization technique, which converge to the unique Nash equilibrium. Finally, we provide error bounds.
joint work with Mario Barela
Electrical circuits with dynamical elements (inductors and capacitors) are implicit differential algebraic equations, and when ideal diodes are included they are differential complementarity problems. The matrices that arise in these problems are symmetric positive definite, which means solutions exist and are unique. These systems can be efficiently solved numerically by high order Diagonally Implicit Runge-Kutta methods in a way that exploits the network structure.