How to subsidize energy efficiency under duopoly efficiently?

Establishing a game theory model, this paper captures the effects of output subsidy on energy efficiency under Cournot competition and Stackelberg competition. Three types of subsidies are considered in the model, namely without subsidy, unilateral subsidy and bilateral subsidy. The findings indicate that firms without subsidy are not willing to improve energy efficiency. Also, subsidy stimulates the subsidized firms' outputs while deters the outputs of other firms. Meanwhile, the equilibrium subsidy intensity depends on firms' position. Furthermore, the minimal subsidy budgets under different situations are presented. Especially, given the fixed subsidy budget, the output of the subsidized firm is the highest if this firm plays the leading position. In addition, certain subsidy can reduce the total emission, while overdue subsidy cannot reach the environmental object.