Allocating common costs of multinational companies based on arm's length principle and Nash non-cooperative game

Allocating common costs among the subsidiaries of multinational companies (MNCs) is widely conducted in practice. It is of paramount importance that optimal allocation plans can be developed. In this study, we propose an allocation method based on the arm's length principle (ALP), which is well accepted for the internal transactions between MNCs and subsidiaries. Unlike the available studies addressing efficiencies, this study considers profits in common cost allocation. We first deduce a general mathematical expression of the ALP for common cost allocation. Based on it, allocation models are developed, aiming to maximize the profits of both MNCs and subsidiaries. We further develop a solution approach including an algorithm based on the Nash non-cooperative game theory. We prove several interesting characteristics of the algorithm, including (i) the algorithm is convergent, (ii) the optimal solution is a Nash equilibrium and unique, and iii) the optimal solution is not affected by any initial allocation plan. The results of a case application highlight the applicability of our allocation method and solution approach. Through the study, we obtain several important practical insights, including (i) both the ALP and cooperate tax rates affect MNCs’ profit maximization, and (ii) subsidiaries’ profit maximization is affected by the ALP only.