This paper illustrates how many partial equilibrium problems with oligopolistic supply can be cast as convex optimization problems rather than mixed complementarity problems as is the current method of choice in the literature. The convex objective can be constructed by adding an appropriate term to a social welfare maximization objective. Adding this Market Power Adjustment (MPA) term creates a convex problem whose KKT-conditions are identical to the Cournot KKT-conditions . The benefits of convex optimization formulations are ease of model formulation, implementation and testing, and, for large problem instances, reduced solution times as convex optimization solvers outperform Mixed Complementarity Problem solvers for large data instances. We discuss stylized examples and present the MPA term for a rather complicated multi energy carrier oligopolistic market model.
Keywords: partial equilibrium, mixed complementarity, multi-level equilibrium, oligopolistic markets, convex optimization, market power