Duopoly game models of water supply in the presence of market power

The purpose of this paper is to investigate the allocation of output and the water supply for two firms to produce differentiated product in two oligopoly game models established under the settings of complete information and incomplete information respectively. By solving a linear demand system model, this paper obtains the corresponding allocation results of output and the water supply for two firms under the condition that the market power exists and the information on the marginal costs is complete. Furthermore, the relation between the allocation result of output and the equilibrium price of water markets in the framework of complete information is analyzed. The study result shows that when the equilibrium price of water markets raises, the total equilibrium output will decrease, while the change rule of the individual output is complicated. Under the condition that water consumption parameters in model are different, and the other parameters in model satisfy suitable conditions, the market shares of output due to the change of the equilibrium price of water markets transforms from the firm who requires more water quantity to the firm who requires less water quantity. Finally, this paper compares the allocation results obtained under the setting of incomplete information on marginal cost with that obtained under the setting of complete information on marginal cost.