Abstract: Under multi-oligopoly competition,mitigation competition considering horizontal cooperation in electricity market is studied using differential game theory. The duopoly competition model proposed by Bass et al. is developed,the carbon emission reduction model of multi-oligopoly competition differential game is constructed,and the optimal on-grid price,initial competitive and horizontal cooperative carbon emission reduction inputs as well as the generators' equilibrium value functions of the model are solved with Hamilton-Jacobi-Bellman equation. In the case of asymmetric generators,the impact of horizontal cooperative carbon emission reduction on market share is considered,and the analytical formula of market share of generators in stable condition is given,which extends the conclusions of Prasad and Sethi on market share. In the case of symmetrical generators,the correlation between the proportion of cooperative carbon emission reduction costs to total carbon emission reduction costs and market share is analyzed,and the parameter constraints satisfied by the optimal number of generators in the market are discussed. The results show that the initial market shares of asymmetric generators are equal,and the generator with the largest cost of carbon emission reduction has the largest market share when it is stable,while the generator with the smallest cost of carbon emission reduction has the smallest stable market share. Even though the initial market shares of symmetrical generators are different,there will not emerge an extreme situation in which a symmetrical generator monopolizes the whole market completely. Instead,each generator tends to undertake the same electric power supply task. Both the duopoly and triopoly electricity markets can always guarantee positive profits for symmetrical generators. Once the number of generators increases to more than three,it will not be guaranteed.

Key words: initial competitive carbon emission reduction, horizontal cooperation, market share, differential game, feedback Nash equilibrium