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Loads of financial difficulties may be formulated as restricted optimizations and equilibration in their ideas. numerous mathematical theories were offering economists with essential machineries for those difficulties coming up in fiscal conception. Conversely, mathematicians were influenced through a variety of mathematical problems raised via monetary theories. The sequence is designed to assemble these mathematicians who're heavily drawn to getting new hard stimuli from financial theories with these economists who're seeking effective mathematical instruments for his or her learn. The editorial board of this sequence includes the next admired economists and mathematicians: Managing Editors : S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors : R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont (CREST-CNRS), N. Hirano (Yokohama nationwide Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Ohio kingdom Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), okay. Kamiya (Univ. Tokyo), ok. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), H. Matano (Univ. Tokyo), ok. Nishimura (Kyoto Univ.), M.K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), A. Yamaguti (Kyoto Univ./Ryukoku Univ.), M. Yano (Keio Univ.).
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Balanced consistency requires that the effect of agent i leaving a queueing problem on the payoff of another agent j ¤ i should be the same as the effect of agent j leaving a queueing problem on the payoff of agent i. 4 Balanced consistency: For all N 2 N ; all Â 2 Q N ; all i; j 2 N; all . Â/; all . ÂNnfig /; and all . ÂNnfjg /, ui . ; t/ ui . j ; t j / D uj . ; t/ uj . i ; t i /: Now we investigate the implications of balanced consistency in the context of queueing problems. First, we show that the minimal transfer rule satisfies the property.
Mutuswami, S. (2009). On the coincidence of the prenucleolus and the Shapley value. Mathematical Social Sciences, 57, 16–25. Kohlberg, E. (1971). On the nucleolus of a characteristic function game. SIAM Journal on Applied Mathematics, 20, 62–66. Maniquet, F. (2003). A characterization of the Shapley value in queueing problems. Journal of Economic Theory, 109, 90–103. Moulin, H. (2007). On scheduling fees to prevent merging, splitting, and transferring of jobs. Mathematics of Operations Research, 32, 266–283.
If jNj D 1; then efficiency implies that i D 1 and ti D 0 for i 2 N. Let N be such that jNj D 2: Without loss of generality, we may assume that N D fi; jg and that Âi Âj : Let . Â/; . ÂNnfig /; and . ÂNnfjg /. By balanced consistency, ui . ; t/ ui . j ; t j / D uj . ; t/ uj . i ; t i /: Since ui . j ; t j / D uj . i ; t i / D 0; we have ui . ; t/ D uj . ; t/: By efficiency, Âj ui . ; t/ C uj . ; t/ D Âj : Altogether, we obtain ui . ; t/ D uj . ; t/ D 2 . By 42 4 Independence, Monotonicity, and Balanced Consistency efficiency and Pareto indifference, we may assume that i D 1 and j D 2.
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