{"title":"Equal Sharing Solutions for Bicooperative Games","authors":"Fan-Yong Meng, Yan Wang","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1947,"pagesEnd":1951,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/4145","abstract":"
In this paper, we discuss the egalitarianism solution (ES) and center-of-gravity of the imputation-set value (CIV) for bicooperative games, which can be seen as the extensions of the solutions for traditional games given by Dutta and Ray [1] and Driessen and Funaki [2]. Furthermore, axiomatic systems for the given values are proposed. Finally, a numerical example is offered to illustrate the player ES and CTV.<\/p>\r\n","references":"[1] B. Dutta and D. Ray, A concept of egalitarianism under participation\r\nconstraints, Econometrica 57 (1989) 615-635.\r\n[2] T. S. H. Driessen and Y. Funaki, Coincidence of and collinearity between\r\ngame theoretic solutions, OR Spektrum 13 (1991) 15-30.\r\n[3] R. van den Brink and Y. Funaki, Axiomatizations of a class of equal\r\nsurplus sharing solutions for TU-games, Theory and Decision 67 (2009)\r\n303-340.\r\n[4] B. Dutta and D. Ray, Constrained egalitarian allocations, Games and\r\nEconomic Behavior 3 (1991) 403-422.\r\n[5] B. Dutta, The egalitarian solution and reduced game properties in convex\r\ngames, International Journal of Game Theory 19 (1990) 153-169.\r\n[6] S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica\r\n57 (1989) 589-614.\r\n[7] M. Davis and M. Maschler, The kernel of a cooperative game, Naval\r\nResearch Logistics Quarterly 12 (1965) 223-259.\r\n[8] J. Arin and E. Inarra, Consistency and egalitarianism: the egalitarian\r\nset, D.P. 163, Dpto. Fundamentos del Analisis Economico UPV-EHU,\r\nSpain, 1997.\r\n[9] F. Klijn, M. Slikker, S. Tijs and J. Zarzuelo, The egalitarian solution for\r\nconvex games: some characterizations, Mathematical Social Sciences 40\r\n(2000) 111-121.\r\n[10] J. Arin, J. Kuipers and D. Vermeulen. Some characterizations of egalitarian\r\nsolutions on classes of TU-games, Mathematical Social Sciences\r\n46 (2003) 327-345.\r\n[11] R. van den Brink, Null or nullifying players: The difference between the\r\nShapley value and equal division solutions, Journal of Economic Theory\r\n136 (2007) 767-775.\r\n[12] H. Salonen, Egalitarian solutions for n-person bargaining games, Mathematical\r\nSocial Sciences 35 (1998) 291-306.\r\n[13] R. Branzei, D. Dimitrov and S. Tijs, Egalitarianism in convex fuzzy\r\ngames, Mathematical Social Sciences 47 (2004) 313-325.\r\n[14] H. Peters and H. Zank, The egalitarian solution for multichoice games,\r\nAnnals of Operations Research 137 (2005) 399-409.\r\n[15] J. M. Bilbao, J. Fernndez, N. Jimnez and J. J. Lpez, The Shapley value\r\nfor bicooperative games, Annals of perations Research 158 (2008) 99-\r\n115.\r\n[16] J. M. Bilbao, J. R. Fernndez, N. Jimnez and J. J. Lpez, The Banzhaf\r\npower index for ternary bicooperative games, Discrete Applied Mathematics\r\n158 (2010) 967-980.\r\n[17] M. Grabisch and C. Labreuche, Bi-capacities-I:definition, Mobius transform\r\nand interaction, Fuzzy sets and systems 151 (2005) 211-236.\r\n[18] X. H. Yu and Q. Zhang, The Shapley value for fuzzy bi-cooperative\r\ngames, International Conference on Intelligent Systems and Knowledge\r\nEngineering 2007.\r\n[19] M. Tsurumi, T. Tanino and M. Inuiguchi, A Shapley function on a class\r\nof cooperative fuzzy games, European Journal of Operational Research\r\n129 (2001) 596-618.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}