Abstract: For government, there are several certain goals considered when distributing carbon quota. For instance, to maximize the total welfare of the society and to minimize the reduction cost. Meanwhile, a certain blue print of distribution reflects government's attitude towards fairness, and it also influences enterprises' production decision, especially between enterprises with different efficiency in reduction. In this paper, under the frame of leader-followers game, the optimal carbon quota allocation strategy when the government realizes multi-objective optimization under taking account of both social welfare and emission reduction costs is studied. We use (p, α)-proportional fairness is used to establish the corresponding relationship between the optimal allocation and the government's attitude towards fairness. And then how enterprises' differences on reduction efficiency influences government's attitude towards fairness is analyzed. Genetic algorithm simulation results show that the government always gives greater quota to high efficiency enterprise when government wants to minimize the reduction cost and to maximize the social welfare. The results also show that how the differences in the efficiency of emission reduction influence the optimal allocation and government's attitude towards fairness will change completely differently within industries with differences between the efficiency of enterprises. When there is a small difference in the efficiency of emission reduction, with the increase of the difference of emission reduction efficiency, the quota of inefficient enterprises gradually decreased, and the government attitude towards fairness is getting smaller and smaller. When the difference in efficiency is larger, the situation is just the opposite. The government paid more attention to fairness, while low-efficiency enterprises get more carbon. Meanwhile, government's attitude towards fairness doesn't mean the low-efficiency enterprise obtain greater quota. As the difference in efficiency in a certain range, the increase in the difference will lead to smaller quota to the low-efficiency enterprise and a higher fairness in allocation. The above-mentioned results provide a useful reference and uncover the superiority of base line method in multi-objective optimization within industry with difference in reduction efficiency. And industries with different reduction efficiency apply to different distribution policy.

Key words: (p, α) proportional fairness, leader-followers game, multi-objective decisions, carbon quota allocation, genetic algorithm