Optimal level of transfer pricing for profit sharing: a Lagrange regularized game theory approach

Abstract

This paper suggests a new game-theoretic method for computing the optimal level of transfer pricing for a multidivisional firm cooperatively organized in multiple controlled divisions. We are considering the transfer pricing problem as a collaborative strategy to reduce global taxation consisting in fixing multidivisional enterprises prices in such a way that a global optimum is attained. The goal is to allocate the firm-wide profit between divisions bearing in mind that transfer prices are globally determined and they are not negotiable. Legal restrictions of the problem correspond to bounds that establish the maximum/minimum transfer price determined by the arm’s length principle and the applicable tax rates. To deal with this problem, this paper suggests a cooperative game theory approach. The solution of the game results in a strong Nash equilibrium. For computing the strong Nash equilibrium we employ a proximal/gradient method. We use a Lagrange regularization approach for ensuring the existence of a unique strong Nash equilibrium for the transfer pricing problem. An application example validates our approach.