cooperative games; bargaining problem; utility theory; voting; social choice.
Subject:
The problem of the existence of countably additive core for cooperative games with countable set of players is solved. The existence theorem for Neumann-Morgenstern solution in each 4-person cooperative game was proved (with O.N.Bondareva and T. E. Kulakovskaya). A number of existence theorems for bargaining sets $M$ in cooperative games were obtained under the assumption that objections and counterobjections are admitted among members of special collections of coalitions. All social welfare orderings on the entire space $R^n$ satisfying scale independence and preserving in the limit conditions are described (with E. B. Yanovskaya). For a fixed arbitrary orthant in $R^n$ each of these orderings is representable by a lexicographical ordering defined by a collection of Cobb–Douglas functions. Vectors from different orthants are compared by a rule based on a linear ordering on the set of orthants and a special number ("depth of comparison") for these orthants. The conditions for commutation of mappings convolving rows and columns of matrices with integer elements and integer values of mappings are obtained. The results generalize Ostrogorski paradox. A number of papers were devoted to axiomatical justification of solutions of bargaining problem with claim point. A complete description of strictly monotonic, consistent and path independent solutions for allocation problem with claims was obtained. This result was applied for axiomatical justification of a class of solutions of bargaining problem with claim points and convex feasible sets including the least square and the maximal weighted entropy solutions.
Biography
Graduated from Faculty of Mathematics and Mechanics of Leningrad state university (Department of probability theory and mathematical statistics). Ph.D. thesis was defended in 1973. A list of my works contains about 50 titles.
Main publications:
Naumova N. I., Yanovskaya E. B. Nash social welfare orderings // Mathematical Social Sciences, 2001, 42(3), 203–231.
Naumova N. I. Nonsymmetric equal sacrifice solutions for claim problem // Mathematical Social Sciences, 2002, 43(1), 1–18.
Natalia I. Naumova, “Computation problems for envy stable solutions of allocation problems with public resources”, Contributions to Game Theory and Management, 14 (2021), 302–311
2019
2.
Natalia I. Naumova, “Envy stable solutions for allocation problems with public resourses”, Contributions to Game Theory and Management, 12 (2019), 261–272
2015
3.
Natalia Naumova, “Generalized nucleolus, kernels, and bargainig sets for cooperative games with restricted cooperation”, Contributions to Game Theory and Management, 8 (2015), 231–242
2014
4.
Natalia Naumova, “An axiomatization of the proportional prenucleolus”, Contributions to Game Theory and Management, 7 (2014), 246–253
2013
5.
Natalia Naumova, “Solidary Solutions to Games with Restricted Cooperation”, Contributions to Game Theory and Management, 6 (2013), 316–337
Natalia I. Naumova, “Generalized Proportional Solutions to Games with Restricted Cooperation”, Contributions to Game Theory and Management, 5 (2012), 230–242
Natalia Naumova, Irina Korman, “Generalized Kernels and Bargainig Sets for Cooperative Games with Limited Communication Structure”, Contributions to Game Theory and Management, 3 (2010), 289–302
2009
9.
Natalia Naumova, “Associated consistency based on utility functions of coalitions”, Mat. Teor. Igr Pril., 1:1 (2009), 87–195
10.
Natalia Naumova, “Associated consistency based on utility functions of coalitions”, UBS, 26.1 (2009), 79–99
2007
11.
Natalia Naumova, “Generalized Kernels and Bargaining Sets for Families of Coalitions”, Contributions to Game Theory and Management, 1 (2007), 346–360
L. M. Brègman, N. I. Naumova, “Arbitration solutions with an ideal point, generated by systems of
functions”, Dokl. Akad. Nauk SSSR, 279:1 (1984), 16–20
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