Characterizations of a Shapley value for multichoice games

ABSTRACT

The main focus of this paper is on a Shapley value for multichoice games introduced by van den Nouweland et al. (ZOR–Math. Meth. Oper. Res. 41 : 289–311, 1995). Here we provide several characterizations from traditional game theory and redefine them in the framework of multichoice games. Meanwhile, the relationship between core and this Shapley value for multichoice games is discussed. When multichoice games are convex, this Shapley value is a multichoice population monotonic allocation scheme (MPMAS).

KEYWORDS:

• Multichoice game
• Shapley value
• core
• MPMAS

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (grant numbers 71571192, 71874112, and 71671188), the Innovation-Driven Project of Central South University (grant number 2018CX039), the Fundamental Research Funds for the Central Universities of Central South University (grant number 2018zzts094), the Major Project for National Natural Science Foundation of China (grant number 71790615), and the State Key Program of National Natural Science of China (grant number 71431006); the Hunan Province Foundation for Distinguished Young Scholars of China (No. 2016JJ1024).

Notes on contributors

Jie Tang

Jie Tang is carrying out her Ph.D. degree in School of Business, Central South University. She received her master degree in School of Management, Qingdao Technological University, China, in 2008. Currently, she has contributed 17 journal articles to professional journals including Information Fusion, Journal of the Operational Research Society, Knowledge-Based Systems, Computers & Industrial Engineering, International Journal of Information Technology & Decision Making, International Journal of Intelligent Systems, Soft Computing, International Transactions in Operational Research, Journal of Intelligent & Fuzzy Systems. Her research interests include uncertain multi-attribute decision making, game theory, cluster analysis and pattern recognition.

Fanyong Meng

Fanyong Meng is a Professor in School of Business, Central South University. He received his master degree in School of Mathematics and Information Science, Guangxi University, China, in 2008, and earned his Ph.D. degree in School of Management and Economics, Beijing Institute of Technology, China, in 2011. He finished his postdoctoral work in School of Business, Central South University, China, in 2016. Currently, he has contributed over 100 journal articles to professional journals such as Omega, Fuzzy Sets and Systems, IEEE Transactions on Systems, Man, and Cybernetics Systems, Applied Mathematics and Computation, Applied Mathematical Modelling, Applied Soft Computing, Computers & Industrial Engineering, Cognitive Computation, Group Decision and Negotiation, Fuzzy Optimization and Decision Making, Information Sciences, Information Fusion, Knowledge-Based Systems, Journal of the Operational Research Society. His research interests include fuzzy mathematics, decision making and game theory.

Qiang Zhang

Qiang Zhang is a professor in the School of Management and Economics, Beijing Institute of Technology. He received his master degree in Department of Probability and Statistics, Beijing University, China in 1978, and earned his Ph.D. degree in School of Traffic and Transportation, Southwest Jiao Tong University, China in 1999. In 2003, he won the operation research newcomer award. Currently, he has contributed over 200 journal articles to professional journals such as European Journal of Operational Research, Fuzzy Sets and Systems, IEEE Transactions on Fuzzy Systems, Information Sciences, Applied Mathematical Modelling. His current research interests include management decisions in quantitative theory and method, game theory, the modern logistics and supply chain management, uncertain system theory and application.