The computation of Cournot–Nash equilibria for the time-definite freight delivery industry under an oligopolistic market

Time-definite freight delivery common carriers provide time-guaranteed door-to-door service for small shipment shippers. For a carrier, the pricing planning problem with inverse demand function requires simultaneous determination of the demand for its service and development of an operating plan to fill the available network capacity in a manner which maximizes its profit. In an oligopolistic market, the Cournot–Nash price equilibrium is all of the carriers achieving the highest individual profit with respect to the market shares and operational plans of the other carriers. This model is applicable to an integral-constrained spatially separated oligopolistic market. We chose the path formulation and proposed a diagonalization algorithm to determine the Cournot–Nash price equilibria. The time-definite freight delivery market in Taiwan was used for numerical testing. The results showed that this approach is suitable for determining the market equilibria for the industry. In addition we discussed the sensitivity on parameters of this approach and the economic implications for carriers.