Baking and slicing the pie: An application to the airline alliance's profit-sharing based on cooperative game theory

Cooperating with competitors can be a mutually beneficial strategy for companies. To achieve continuous gains from the partnership, profit-sharing rules for the collective benefits are critical. This paper proposes a new allocation scheme that focuses on sustainable relationships based on cooperative game theory. Our min-variance solution deploys joint profits by minimizing the intent to form sub-groups, thus ensuring the alliance's stability. The min-variance is reasonable in a network collaboration where the preservation of the network itself is essential. By application to a numerical example of an airline joint venture, we examine the validity of the proposed distribution rule in the cooperation-allocation problem. The collective surplus of logistics collaboration is suggested by a mixed-integer programming model to solve the optimal value of combinations of the multi-commodity flow problem under the network shared. In addition, the results are interpreted by comparison with other solutions in cooperation game theory, such as the Shapley value, the τ–value, and the nucleolus. We offer further insights into changes in profit-sharing using a sensitivity analysis considering efficiency abatement.