Abstract: In a two-tier supply chain consisting of a single supplier and multiple retailers, the collaborative ordering decisions for the multi-retailers under the carbon trading mechanism are studied. In the full information situation, the cost allocation problem among retailers are studied in the framework of cooperative game theory. The corresponding cooperative games are established and are proved to be submodular games, and allocation rules which can be realized by the population monotonic allocation scheme are proposed. Moreover, the stability of the grand coalition is analyzed using the concept of the largest consistent set. For cost allocation problem with incomplete information, the existence of the pure strategy Nash equilibrium is proved. The results show that collaboration among retailers not only reduces the total cost, but also reduces the carbon emissions. However, the cost shared by the retailers in the incomplete information situation is more than that in the full information situation.

Key words: carbon cap and trade, cooperative game, core, largest consistent set, Nash equilibrium