Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
cooperative games; cooperative fuzzy games; restricted games; coalitions
cooperative games; cooperative fuzzy games; restricted games; coalitions
Summary:
Cooperative games are very useful in considering profit allocation among multiple decision makers who cooperate with each other. In order to deal with cooperative games in practical situations, however, we have to deal with two additional factors. One is some restrictions on coalitions. This first factor has been taken into consideration through feasibility of coalitions. The other is partial cooperation of players. In order to describe this second factor, we consider fuzzy coalitions which permit partial participation in a coalition to a player. In this paper we take both of these factors into account in cooperative games. Namely, we analyze and discuss cooperative fuzzy games extended from ordinary cooperative games with restrictions on coalitions in two approaches. For the purpose of comparison of these two approaches, we define two special classes of extensions called $U$-extensions which satisfy linearity and $W$-extensions which satisfy $U$-extensions and two additional conditions, restriction invariance and monotonicity. Finally, we show sufficient conditions under which these obtained games in two approaches coincide.
References:
[1] Algaba E., Bilbao J. M., Lopez J.: A unified approach to restricted games. Theory and Decision 50 (2001), 333–345 DOI 10.1023/A:1010344404281 | MR 1845886 | Zbl 1039.91003
[2] Aubin J. P.: Mathematical Methods of Game and Economic Theory. North–Holland, Amsterdam 1979 MR 0556865 | Zbl 1152.91005
[3] Bilbao J. M.: Cooperative Games on Combinatorial Structures. Kluwer Academic Publishers, Boston 2000 MR 1887284 | Zbl 0983.91013
[4] Brânzei R.: Convex fuzzy games and partition monotonic allocation schema. Fuzzy Sets and Systems 139 (2003), 267–281 MR 2006775
[5] Lovász L.: Submodular functions and convexity. In: Mathematical Programming: The State of the Art (A. Bachem et al., eds.), Springer–Verlag, Berlin 1983, pp. 235–257 MR 0717403 | Zbl 0566.90060
[6] Mareš M.: Fuzzy Cooperative Games. Physica–Verlag, Heidelberg 2001 MR 1841340 | Zbl 1037.91007
[7] Moritani A., Tanino T., Kuroki, K., Tatsumi K.: Cooperative fuzzy games with restrictions on coalitions. In: Proc. Third Internat. Conference on Nonlinear Analysis and Convex Analysis 2004, pp. 323–345 MR 2144055 | Zbl 1149.91016
[8] Nishizaki I., Sakawa M.: Fuzzy and Multiobjective Games for Conflict Resolution. Physical–Verlag, Heidelberg 2001 MR 1840381 | Zbl 0973.91001
[9] Owen G.: Multilinear extensions of games. Management Sci. 18 (1972), 64–79 DOI 10.1287/mnsc.18.5.64 | MR 0294010 | Zbl 0239.90049
[10] Tanino T.: Cooperative fuzzy games as extensions of ordinary cooperative games. In: Proc. 7th Czech–Japan Seminar on Data Analysis and Decision Making under Uncertainty (H. Noguchi, H. Ishii, M. Inuiguchi, eds.), Awaji Yumebutai ICC 2004, pp. 26–31
Search
Partner of
