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Resource sharing and payoff allocation in a three-stage system: Integrating network DEA with the Shapley value method

Qingxian An,Yao Wen,T. Ding,Yongli Li

Published 2019 in Omega

ABSTRACT

Abstract Resource sharing exists not only among multiple entities but also among various stages of a single network structure system. Previous studies focused on how to allocate total given sharable resources to stages to maximize the efficiency of the network structure system, and a few discussed the fair allocation of potential gains obtained from resource sharing. In this study, we explore a new case in which the common inputs (or shared resources) of all stages are known. By constructing a game that regards each stage as a player, we integrate cooperative game theory with network data envelopment analysis (DEA) to explore the payoff allocation problem in a three-stage system. We build network DEA models to calculate the optimal profits of the system before and after resource sharing (i.e., pre- and post-collaboration optimal profits), and then apply the Shapley value method to allocate the increased profits of the system to its stages. Results indicate that the game among stages in a three-stage system is superadditive. A numerical example is provided to illustrate our method.

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