×

zbMATH — the first resource for mathematics

On some families of cooperative fuzzy games. (English) Zbl 1128.91005
Let \((Q, v)\) be a fuzzy game. This paper surveys, with proofs, the main results learned about fuzzy games since their introduction by Aubin (1979). Among the results proved for fuzzy games are the following: if a fuzzy game is strongly superadditive, it has a non-empty core; if a fuzzy game is convex, it has a large core; if a fuzzy game is exact, then its core is a stable set.

MSC:
91A12 Cooperative games
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
Keywords:
core; convex games
PDF BibTeX XML Cite
Full Text: DOI Link
References:
[1] Aubin JP (1979) Mathematical methods of game and economic theory. North-Holland, Amsterdam · Zbl 0452.90093
[2] Aubin JP (1981a) Cooperative fuzzy games. Math Oper Res 6:1–13 · Zbl 0496.90092
[3] Aubin JP (1981b) Locally Lipschitz cooperative games. J Math Econ 8:241–262 · Zbl 0461.90086
[4] Azrieli Y, Lehrer E (2005) Extendable cooperative games. J Public Econ Theory (in press) · Zbl 1128.91005
[5] Azrieli Y, Lehrer E (2007) Market games in large economies with a finite number of types. Econ Theory 31:327–342 · Zbl 1172.91303
[6] Biswas A, Parthasarathy T, Potters JAM, Voorneveld M (1999) Large cores and exactness. Games Econ Behav 28:1–12 · Zbl 0957.91009
[7] Bondareva O (1962) The theory of the core in an n-person game (in Russian). Vestnik Leningrad Univ 13:141–142 · Zbl 0122.15404
[8] Branzei R, Dimitrov D, Tijs S (2003) Convex fuzzy games and participation monotonic allocation schemes. Fuzzy Sets Syst 139:267–281 · Zbl 1065.91006
[9] Branzei R, Dimitrov D, Tijs (2005) Models in cooperative game theory: crisp, fuzzy and multi-choice games. In: Lecture notes in economics and mathematical systems, vol 556. Springer, Heidelberg · Zbl 1079.91005
[10] van Gellekom JRG, Potters JAM, Reijnierse JH (1999) Prosperity properties of TU-games. Int J Game Theory 28:211–227 · Zbl 0941.91008
[11] Husseinov F (1994) Interpretation of Aubin’s fuzzy coalitions and their extension. J Math Econ 23:499–516 · Zbl 0834.90033
[12] Kikuta K, Shapley LS (1986) Core stability in n-person games (Unpublished paper)
[13] Rockafellar RT (1997) Convex analysis. Princeton university press, Princeton · Zbl 0932.90001
[14] Schmeidler D (1972) Cores of exact games I. J Math Anal Appl 40:214–225 · Zbl 0243.90071
[15] Shapley LS (1967) On balanced sets and cores. Nav Res Log Q 14:453–460
[16] Shapley LS (1971) Cores of convex games. Int J Game Theory 1:11–26 · Zbl 0222.90054
[17] Sharkey WW (1982) Cooperative games with large cores. Int J Game Theory 11:175–182 · Zbl 0494.90096
[18] Sharkey WW, Telser LG (1978) Supportable cost functions for the multiproduct firm. J Econ Theory 18:23–37 · Zbl 0397.90019
[19] Tijs S, Branzei R (2004a) Various characterizations of convex fuzzy games. Top 12:399–408 · Zbl 1109.91011
[20] Tijs S, Branzei R, Ishihara S, Muto S (2004b) On cores and stable sets for fuzzy games. Fuzzy Sets Syst 146:285–296 · Zbl 1099.91015
[21] Tsurumi M, Tanino T, Inuiguchi M (2001) A Shapley function on a class of cooperative fuzzy games. Eur J Oper Res 129:596–618 · Zbl 1125.91313
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.