The Maschler–Perles–Shapley value for Taxation Games

We continue the discussion of the taxation game following our presentation in [12]. Our concept describes a cooperative game played between a set of jurisdictions (“ countries”). These players admit the operation of a multinational enterprise (MNE, the “firm”) within their jurisdiction. The original version of this game is due to W. F. Richter [3],[4]. We suggest an extension of the model by introducing the dual game of the firm’s profits and the tax function game. The latter is the NTU game generated by introducing tax functions (the term “tariffs” will be avoided henceforth). In [12] we treated the bargaining situation obtained when all countries decide to cooperate – otherwise everyone will fall back on their status quo point. However, in his basic paper, Richter argues that the share of the tax basis allotted to a country should be determined by the Shapley value of the taxation game. This idea establishes an interesting new field of applications. The Shapley value “as a tool in theoretical economics” [13], [14] has widely been applied in Game Theory, Equilibrium Theory, applications to Cost Sharing problems, Airport Landing Fee games, and many others. Based on these ideas, we continue our presentation by formulating the tax function game for the countries involved and introducing the Maschler–Perles–Shapley value as developed in [11]. To this end, we introduce the adjusted TU game, which reflects a rescaling of utility measurement as suggested by the superadditivity axiom of the Maschler–Perles solution. Then the Maschler–Perles–Shapley value of the tax function game is the image of the Shapley value of the adjusted TU game on the Pareto surface of the grand coalition. We demonstrate that the Maschler-Perles–Shapley value for the tax function game is Pareto efficient, covariant with affine transformations of utility, and anonymous.