In the past decades, there has been a worldwide multilateral efforts to reduce carbon emissions. In particular, the "cap-and-trade" mechanism has been regarded as an effective way to control emissions. This is a market-based approach focused on the efficient allocation of initial emissions allowances. Based on the "grandfather" allocation method, this paper develops an alternative method derived from Boltzmann distribution to calculate the allowances. Further, with fully considering the relationship between the regional authority, power plants and grid company, a three-level multi-objective model for carbon emission allowance allocations in the power-supply industry is presented. To achieve tripartite equilibrium, the impacts on electricity output, carbon emissions and carbon intensity of the allocation method, allocation cap, and emission limits are assessed. The results showed that the greatest impact was seen in the emission limits rather than the allocation cap or allocation method. It also indicated that to effectively achieve reduction targets, it is necessary to allocate greater allowances to lower carbon intensity power plants. These results demonstrated the practicality and efficiency of the proposed model in seeking optimal allocation policies. (c) 2015 Elsevier Ltd. All rights reserved.