Equivalence theorem, consistency and axiomatizations of a multi-choice value

  • Yan-An Hwang
  • Yu-Hsien Liao


This paper is devoted to the study of solutions for multi-choice games which admit a potential, such as the potential associated with the extended Shapley value proposed by Hsiao and Raghavan (Int J Game Theory 21:301–302, 1992; Games Econ Behav 5:240–256, 1993). Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it is shown that each of these solutions can be obtained by applying the extended Shapley value to an appropriately modified game. In the framework of multi-choice games, we also provide an extension of the reduced game introduced by Hart and Mas-Colell (Econometrica 57:589–614, 1989). Different from the works of Hsiao and Raghavan (1992, 1993), we provide two types of axiomatizations, one is the analogue of Myerson’s (Int J Game Theory 9:169–182, 1980) axiomatization of the Shapley value based on the property of balanced contributions. The other axiomatization is obtained by means of the property of consistency.


Multi-choice games Shapley value Potential Balanced contributions Consistency 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Dong Hwa UniversityHualienTaiwan, ROC
  2. 2.Department of MathematicsChung Jen College of Nursing, Health Science and ManagementChia YiTaiwan, ROC

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