Multi-objective linear programming games and applications in supply chain competition

In this paper, we study a class of multi-player multi-objective game models with linear objectives. Based on the duality theory and Karush-Kuhn-Tucker (KKT) conditions, two approaches for solving the model are proposed, respectively. For the duality based approach, we show that solving Pareto equilibrium of the primal problem is equivalent to solving a multi-linear system. As to the KKT based approach, we prove that Pareto equilibrium can be achieved by solving a linear complementarity problem. As an application, we investigate supply chain competition problem using the underlying game model, which is further solved by these two approaches. Preliminary numerical test is conducted to demonstrate the efficiency of the presented approaches.