Foundations of Lexicographic Cooperative Game Theory
Автор: Guram N. Beltadze
Журнал: International Journal of Modern Education and Computer Science (IJMECS) @ijmecs
Статья в выпуске: 3 vol.5, 2013 года.
Бесплатный доступ
In the article dimensional lexicographic noncooperative games are defined for the players' for which there exists a characteristic function . Some main features are proved of function in a lexicographic case. A lexicographic cooperative game is called a couple, whereis a real vector-function on subsets and the following conditions are fulfilled =O; Such cooperative game is denoted by . imputation and its set is defined in game. It is proved that is nonempty and its full characterisation is given. Domination over set is defined. Thus, the main foundations are given, according to this, it is possible to explore the main principles of optimality.
Game, Lexicography, Noncooperative Game, Cooperative Game, Imputation, Domination
Короткий адрес: https://sciup.org/15014528
IDR: 15014528
Список литературы Foundations of Lexicographic Cooperative Game Theory
- P. C. Fishburn, "On the foundations of game theory: the case of non-Arximedean utilites", Internat. J. Game Theory, 1, № 2 (1972), pp. 65-71.
- V. V. Podinovski, "Lexicographic games", Advances in game theory (Proc. Second All- Union Conf. Vilnius 1971), Izdat. "Mintis", Vilnius, (1973). pp. 100-103 (in Russian).
- G.N. Beltadze, "A mixed extension of finite noncoalition lexicographic games", Bulletin of the Academy of sciences of the Georgian SSR, 98, № 2 (1980), pp. 273-276 (in Russian).
- G.N. Beltadze, J.A.Giorgobiani, "Metastrategic extensions of Lexicographic Noncooperative Gamein case of two players", Bulleten of the Georgian National Academy of Sciences, vol 2, no 2, 2008, pp. 9-13.
- M. Salukvadze, G. Beltadze and F. Criado, "Dyadic theoretical games models of decision - making for the lexicographic vector payoffs", International Journal of Information Technology and Decision Making, Vol. 8, Issue 2, 2009, pp. 193-216.
- G. N Beltadze, "Lexicographic noncooperative game's mixed extension with criteria", International Journal of Systems and Software, Asian Research Publishing Network (ARPN) Publishers, Vol 1, № 8, November 2011, pp. 247-250.
- G.N. Beltadze, "Lexicographic Multistage Games With Perfect Information", Informational and Communication Technologies – Theory and Practice: Proceedings of the International Scientific Conference, ICTMC-2010 Devoted to the 80th Anniversary of I.V. Prangishvili, Nova Publishers, 664 p. USA, 2012, pp. 275-281.
- G.N. Beltadze, "Cooperative games with lexicographic payoffs", Bulletin of the Academy of sciences of the Georgian SSR, 99, № 2 (1980), pp. 309 -312 (in Russian).
- J. von Neuman, O. Morgenstern, "Theory of Games and Economic Behavior", Prinston University Press, 1944.