Cooperative performance evaluation among homogeneous parallel decision making units with coalition structures

For large groups like chain hotels, internal cooperation among subsidiaries and external cooperation among groups are both important strategies to increase profits. To fight for more superiority in payoff allocation, the subsidiaries in a group usually make up a prior union in the form of internal cooperation such as resource sharing and information sharing. In data envelopment analysis (DEA), many studies discuss the external cooperation among independent decision making units (DMUs) based on cooperative game theory, but few simultaneously consider the information sharing among network structure DMUs and information and resource sharing among internal sub-units. How to evaluate the cooperative performance among large groups with different subsidiaries and how to allocate joint payoff? To answer this question, we construct a cooperative game with coalition structures, named the DEA game with coalition structures. We view groups as homogeneous parallel DMUs and their subsidiaries as sub-units. In our proposed game, each DMU is a prior union where sub-units are players. Through the network DEA, we measure the cooperative performance from the perspective of relative efficiency. Based on cooperative game theory, we demonstrate our game is balanced, super-additive and monotone, and one payoff allocation in the coalitional core can be found by calculating the dual programming for the grand coalition. Furthermore, we use the two-step Shapley value to allocate the overall payoff of the grand coalition to sub-units. Finally, we verify our approach by experimenting with the operational data of seven international star quality and high-end chain hotels in Taiwan in 2015.