A Log-domain Interior Point Method for Convex Quadratic Games

Abstract

In this paper, we propose an equilibrium-seeking algorithm for finding generalized Nash equilibria of non-cooperative monotone convex quadratic games. Specifically, we recast the Nash equilibrium-seeking problem as variational inequality problem that we solve using a log-domain interior point method and provide a general purpose solver based on this algorithm. This approach is suitable for non-potential, general sum games and does not require extensive structural assumptions. We demonstrate the efficiency and versatility of our method using three benchmark games and demonstrate our algorithm is especially effective on small to medium scale problems.