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Transformation of Characteristic Function in Dynamic Games

Abstract The problem of transformation of characteristic function, using a transformation matrix and connected with associated consistency of a solution concept, was investigated for the class of so-called “one-shot” games. The same problem also arises in dynamic games when players move step by step along the cooperative trajectory. In this case the evolution of characteristic function is, in general, unpredictable and may lead to time-inconsistency of a fixed cooperative solution concept. There are different approaches to overcome this problem based on transformation of characteristic function. In this paper, the step-wise transformation is used, which is a generalization of similar transformation of characteristic function for dynamic games with perfect information, and it leads to the time-consistent solution. The general form of such transformation is proposed.