Title: Profit allocation scheme among partners in virtual enterprises based on Shapley values with fuzzy payoffs

Authors: Wen Chen, Qiang Zhang, Mingzhe Wang

Addresses: Department of Management and Economics, Beijing Institute of Technology, Beijing 100081, PR China. ' Department of Management and Economics, Beijing Institute of Technology, Beijing 100081, PR China. ' Department of Management and Economics, Beijing Institute of Technology, Beijing 100081, PR China

Abstract: Virtual enterprises (VE) can be viewed as a cooperative alliance of member companies. An important part of the operation of VE is how to allocate the profit among partners in uncertain environment. This case can be viewed as a fuzzy cooperation game. In this paper, we make a study of the Shapley values with the fuzzy payoff functions from the viewpoint that the payoffs of each coalition are often only imprecisely or ambiguously known to the players. Axioms of the classical Shapley value are extended to the fuzzy Shapley values. From the viewpoint that the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, we proposed a crisp allocation scheme based on fuzzy Shapley values.

Keywords: virtual enterprises; cooperative games; fuzzy payoffs; Shapley values; extension principle; uncertainty; profit allocation; fuzzy cooperation; crisp allocation.

DOI: 10.1504/IJLEG.2007.014494

International Journal of Logistics Economics and Globalisation, 2007 Vol.1 No.1, pp.49 - 62

Published online: 11 Jul 2007 *

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