A jointly constrained bilinear programming method for solving generalized Cournot-Pareto models

We propose a vector optimization approach to linear Cournot oligopolistic market equilibrium models where the strategy sets depend on each other. We use scalarization technique to find a Pareto efficient solution to the model by using a jointly constrained bilinear programming formulation. We then propose a decomposition branch-and-bound algorithm for globally solving the resulting bilinear problem. The subdivision takes place in one-dimensional intervals that enables solving the problem with relatively large sizes. Numerical experiments and results on randomly generated data show the efficiency of the proposed algorithm.