On the Grey Equal Surplus Sharing Solutions

Document Type: Research Paper

Authors

1 Süleyman Demirel University, Isparta, Turkey

2 Usak University, Usak, Turkey

Abstract

The grey uncertainty is a new methodology focusing on the study of problems involving small samples and poor information. It deals with uncertain systems with partially known information through generating, excavating, and extracting useful information from what is available. This paper focuses some division solutions for cooperative games, called the equal surplus sharing solutions. A situation, in which a finite set of players can obtain certain grey payoffs by cooperation can be described by a cooperative grey game. In this paper, we consider some grey division rules, namely the equal surplus sharing grey solutions. Further, we focus on a class of equal surplus sharing grey solutions consisting of all convex combinations of these solutions. An application from Operations Research (OR) situations is also given.

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Main Subjects


Alparslan Gok S.Z., Branzei R. and Tijs S., (2009a). Convex interval games. Journal of Applied Mathematics and Decision Sciences, 2009, Article ID 342089, 14 pages, DOI: 10.1115/2009/342089.

Alparslan Gok S.Z., Miquel S. and Tijs S., (2009b). Cooperation under interval uncertainty. Mathematical Methods of Operations Research, Vol. 69, pp. 99-109.

Alparslan Gok S.Z., Branzei O., Branzei R. and Tijs S., (2011). Set-valued solution concepts using interval-type payoffs for interval games, Journal of Mathematical Economics, Vol.47, pp. 621-626.

Borm P., Hamers H. and Hendrickx R., (2001). Operations Research games: A survey. TOP, Vol.9, pp. 139-216.

Branzei R., Dimitrov D. and Tijs S., (2008). Models in Cooperative Game Theory. Game Theory and Mathematical Methods, Springer, Berlin, Germany.

Deng J., (1982). Control problems of Grey Systems, Systems and Control Letters, Vol.5, pp. 288-294.

Driessen T.S.H. and Funaki Y., (1991). Coincidence of and collinearity between game theoretic solutions. OR Spektrum, Vol. 13, pp. 15-30.

Moore R., (1979). Methods and applications of interval analysis, SIAM, Philadelphia.

Nisan N., Roughgarden T., Tardos É. and Vazirani V.V., (2007). Algorithmic Game Theory, Cambridge, UK: Cambridge University Press, ISBN 0-521-87282-0.

Palanci O., Alparslan Gok S.Z., Ergun S. and Weber G.-W., (2015). Cooperative grey games and the grey Shapley value, Optimization: A Journal of Mathematical Programming and Operations Research, Vol. 64(8), pp. 1657-1668.

Palanci O. and Alparslan Gok S.Z., (2017). Facility Location Situations and Related Games in Cooperation. Spatial Interaction Models, Vol. 118 (The series Springer Optimization and Its Applications), pp. 247-260.

Tijs S., (2003). Introduction to Game Theory, Hindustan Book Agency, India.

Van den Brink R. and Funaki Y., (2009). Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games, Theory and Decision, Vol. 67(3), pp. 303-340.