Time consistent shapley value imputation for cost-saving joint ventures

As markets become increasingly globalized and firms become more multinational, corporate joint ventures are likely to yield opportunities to quickly create economies of scale and critical mass, and facilitate rational resource sharing. A major source of gain from joint venture is from cost savings. However, it is often observed that after a certain time of cooperation, some firms may gain sufficient skills and technology that they would do better by breaking up from the joint venture. This is the well-known problem of time inconsistency. In this paper, we consider a dynamic cost saving joint venture which adopts the Shapley value as its profit allocation scheme. A compensation mechanism distributing payments to participating firms at each instant of time is devised to ensure the realization of the Shapley value imputation throughout the venture duration. Hence time-consistency will be attained, and a dynamically stable joint venture can be formed.