An Improved Algorithm of Integer Programming to Solve the Cournot Model

Nash Equilibrium is the solution of the Cournot Model considering the reaction functions provided that outputs are successive. However in practice, the outputs of some products are not successive. An improved branch and bound algorithm is proposed combining the Nash Equilibrium, considering the discontinuous output. The proposed algorithm is different from the traditional algorithm where the respond functions would be converted into constrains. While the improved algorithm is used to calculate the output of each manufacturer, the worst solution arising in the mid-process of calculation will be removed firstly, and then the final common integer solution of all manufactures will be the optimal solution. The procedure of the proposed algorithm is explicated in this paper. An example where two manufactures exist is studied, and the results validate the effectiveness of the method.