Data envelopment analysis

Biology

Stochastic game

Microeconomics

Resource allocation

Economics

Cooperative game theory

Computer science

Mathematical optimization

Shared resource

Computer network

Paleontology

Operations research

Mathematics

Value (mathematics)

Stage (stratigraphy)

Mathematical economics

Game theory

Superadditivity

Shapley value

Machine learning

Resource (disambiguation)

Omega

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.

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