Cooperative Grey Games: Grey Solutions and an Optimization Algorithm

Document Type : Research Paper


1 Suleyman Demirel University, Isparta, Turkey

2 Institute of Applied Mathematics, Middle East Technical University and Poznan University of Technology, Poznan, Poland


In this paper, some set-valued solutions using grey payoffs, namely, the grey core, the grey dominance core and the grey stable sets for cooperative grey games, are introduced and studied. Our main results contained are relations between the grey core, the grey dominance core and the grey stable sets of such a game. Moreover, we present a linear programming (LP) problem for the grey core. On the other hand, we suggest a corresponding optimization-based
algorithm finding the grey core element of a cooperative grey game. Finally, we give an application how cooperative grey game theory can be used to model users' behaviors in various multimedia social networks. The paper ends with a
conclusion and an outlook to future investigations.


Main Subjects

Bockarjova Z.M., Sauhats A., Vempers G. and Tereskina I., (2010). On application of the cooperative game theory to energy supply system planning. Energy Market (EEM): 7th International Conference on the European, Madrid, Spain, June 23-25, pp. 1-6.
Bondareva O.N., (1963). Certain applications of the methods of linear programming to the theory of cooperative games. Problemly Kibernetiki, Vol.10, pp. 119-139 (in Russian).
Chen W., Liu Z., Sun X. and Wang Y. (2010). A game-theoretic framework to identify overlapping communities in social networks. Data Mining and Knowledge Discovery, Vol. 21(2), pp. 224-240.
Deng J., (1982). Control problems of Grey Systems. Systems and Control Letters, Vol.5, pp. 288-294.
Deng J., (1985). Grey System Fundamental Method. Huazhong University of Science and Technology, Wuhan, China.
Ekici M., Palanci O. and Alparslan Gök S.Z. (2018). The grey Shapley value: an axiomatization, IOP Conference Series: Materials Science and Engineering, Vol. 300, pp. 1-8.
Fang Z. and Liu S.F., (2003). Grey matrix game model based on pure strategy. Journal of Nanjing University of Aeronautics & Astronautics, Vol. 35(4), pp. 441-445.
Gilles R.P., (2010). The cooperative game theory of networks and hierarchies. In Theory and Decision Library C, 1st edition, 44, Springer, Heidelberg.
Goel A. and Ronaghi F., (2012). A game-theoretic model of attention in social networks. In International Workshop on Algorithms and Models for the Web-Graph, pp. 78-92, Springer Berlin Heidelberg.
Alparslan Gök S.Z., Palanci O. and Yücesan Z. (2018). Peer Group Situations and Games with Grey Uncertainty. Handbook of Research on Emergent Applications of Optimization Algorithms, Chapter 11, pp. 265-278, IGI Global, USA.
Kleinberg J. and Tardos É., (2008). Balanced outcomes in social exchange networks. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pp. 295-304, ACM.
Kose E. and Forest J.Y.L., (2015). N-person grey game, Kybernetes, Vol. 44(2), pp. 271-282.
Li G.P., Pan Z.S, Xiao B. and Huang L.W., (2014). Community discovery and importance analysis in social network. Intelligent Data Analysis, Vol. 18, pp. 495-510.
Liu S. and Lin Y., (2006). Grey Information: Theory and Practical Applications, Springer, London.
Liu W., Li W. and Yue K., (2007). Intelligent Data Analysis, Science Press, Beijing.
Moore R., (1979). Methods and applications of interval analysis, SIAM, Philadelphia.
Narahari Y. and Narayanam R., (2011a). Tutorial: Game Theoretic Models for Social Network Analysis.
Narayanam R. and Narahari Y., (2011b). Topologies of strategically formed social networks based on a generic value function-Allocation rule model. Social Networks, Vol. 33(1), pp. 56-69.
Narayanam R. and Narahari Y., (2011c). A shapley value-based approach to discover influential nodes in social networks. IEEE Transactions on Automation Science and Engineering, Vol. 8(1), pp. 130-147.
Palanci O., Alparslan Gök S.Z., Ergün 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.
Roy S.K., Maity G., Weber G.W. and Alparslan Gök S.Z., (2016). Conic Scalarization Approach to Solve Multi-choice Multi-objective Transportation Problem with Interval Goal. Annals of Operations Research (ANOR); DOI 10.1007/s10479-016-2283-4.
Saad W., Han Z., Debbah M., Hjorrungnes A. and Basar T., (2009). Coalitional game theory for communication networks: a tutorial, Signal Processing Magazine. IEEE Transactions on Automation Science and Engineering, Vol. 26, pp. 77-97.
Scott J., (2012). Social network analysis. Sage.
Shapley L.S., (1967). On balanced sets and cores. Naval Research Logistics Quarterly, Vol. 14, pp. 453-460.
Terlutter R. and Capella M.L., (2013). The gamification of advertising: analysis and research directions of in-game advertising, advergames, and advertising in social network games. Journal of Advertising, Vol. 42(2-3), pp. 95-112.
Tijs S., (2003). Introduction to Game Theory. Hindustan Book Agency, India.
von Neumann J. and Morgenstern O., (1944). Theory of Games and Economic Behavior. Princeton Univ. Press, Princeton NJ.
Zhang J.J., Wu D.S. and Olson D.L., (2005). The method of grey related analysis to multiple attribute decision making problems with interval numbers. Mathematical and Computer Modelling, Vol. 42(9-10), pp. 991-998.