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Weakly Stable Sets of NTU Game
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
College of Mathematics, Qingdao University, Qingdao, China
- 1 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
- 2 College of Mathematics, Qingdao University, Qingdao, China
American Journal of Operations Research·Volume 02 (2012)·Pages 91–93·Published 14 March 2012·DOI10.4236/ajor.2012.21010
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Abstract
In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core, the weakly stable set and the refined core.
KeywordsNTU GameWeak DominanceCoreWeakly Stable Set
- R. J. Aumann, “An Axiomatization of the Non-Transferable Utility Value,” Econometrica, Vol. 53, No. 3, 1985, pp. 599-612. doi:10.2307/1911657
- U. Faigle and W. Kern, “The Shapley Value for Cooperative Games under Precedence Constraints,” International Journal of Game Theory, Vol. 21, No. 3, 1992, pp. 249- 266. doi:10.1007/BF01258278
- J. V. Neumann and O. Morgenstern, “Theory of Games and Economic Behavior,” Princeton University Press, Princeton, 1944.
- H. W. Gao, “On the Weakly Stable Sets of Cooperative Games,” Journal of Qingdao University, Vol. 11, No. 4, 1998, pp. 1-5.
- P. E. M. Borm and S. H. Tijs, “Strategic Claim Games Corresponding to an NTU-Game,” Games and Economic Behavior, Vol. 4, No. 1, 1992, pp. 58-71. doi:10.1016/0899-8256(92)90005-D
- J. C. Harsanyi, “A Simplified Bargaining Model for the n-Person Cooperative Game,” International Economic Review, Vol. 4, No. 2, 1963, pp. 194-207. doi:10.2307/2525487
- L. S. Shapley and M. Shubik, “On Market Games,” Journal of Economic Theory, Vol. 1, No. 1, 1969, pp. 9-25. doi:10.1016/0022-0531(69)90008-8
- E. Kalai and D. Samet, “Unanimity Games and Pareto Optimality,” International Journal of Game Theory, Vol. 14, No. 1, 1985, pp. 41-50. doi:10.1007/BF01770226
- M. Maschler and G. Owen, “The Consistent Shapley Value for Games without Side Payments,” In: R. Selten, Ed., Rational Interaction, Springer-Verlag, Berlin, 1992, pp. 5-12.
- S. Hart, “A Comparison of Non-Transferable Utility Values,” Theory and Decision, Vol. 56, No.1-2, 2004, pp. 35- 46. doi:10.1007/s11238-004-5633-7
- R. P. Lejano, “A Note on Solution Concepts for Nontransferable Utility Games,” Journal of Mathematical Economics, Vol. 47, No. 6, 2011, pp. 777-780. doi:10.1016/j.jmateco.2011.10.001