Abstract
In a fuzzy cooperative game the players may choose to partially participate in a coalition. A fuzzy coalition consists of a group of participating players along with their participation level. The characteristic function of a fuzzy game specifies the worth of each such coalition. This paper introduces well-known properties of classical cooperative games to the theory of fuzzy games, and studies their interrelations. It deals with convex games, exact games, games with a large core, extendable games and games with a stable core.
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References
Aubin JP (1979) Mathematical methods of game and economic theory. North-Holland, Amsterdam
Aubin JP (1981a) Cooperative fuzzy games. Math Oper Res 6:1–13
Aubin JP (1981b) Locally Lipschitz cooperative games. J Math Econ 8:241–262
Azrieli Y, Lehrer E (2005) Extendable cooperative games. J Public Econ Theory (in press)
Azrieli Y, Lehrer E (2007) Market games in large economies with a finite number of types. Econ Theory 31:327–342
Biswas A, Parthasarathy T, Potters JAM, Voorneveld M (1999) Large cores and exactness. Games Econ Behav 28:1–12
Bondareva O (1962) The theory of the core in an n-person game (in Russian). Vestnik Leningrad Univ 13:141–142
Branzei R, Dimitrov D, Tijs S (2003) Convex fuzzy games and participation monotonic allocation schemes. Fuzzy Sets Syst 139:267–281
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
van Gellekom JRG, Potters JAM, Reijnierse JH (1999) Prosperity properties of TU-games. Int J Game Theory 28:211–227
Husseinov F (1994) Interpretation of Aubin’s fuzzy coalitions and their extension. J Math Econ 23:499–516
Kikuta K, Shapley LS (1986) Core stability in n-person games (Unpublished paper)
Rockafellar RT (1997) Convex analysis. Princeton university press, Princeton
Schmeidler D (1972) Cores of exact games I. J Math Anal Appl 40:214–225
Shapley LS (1967) On balanced sets and cores. Nav Res Log Q 14:453–460
Shapley LS (1971) Cores of convex games. Int J Game Theory 1:11–26
Sharkey WW (1982) Cooperative games with large cores. Int J Game Theory 11:175–182
Sharkey WW, Telser LG (1978) Supportable cost functions for the multiproduct firm. J Econ Theory 18:23–37
Tijs S, Branzei R (2004a) Various characterizations of convex fuzzy games. Top 12:399–408
Tijs S, Branzei R, Ishihara S, Muto S (2004b) On cores and stable sets for fuzzy games. Fuzzy Sets Syst 146:285–296
Tsurumi M, Tanino T, Inuiguchi M (2001) A Shapley function on a class of cooperative fuzzy games. Eur J Oper Res 129:596–618
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Azrieli, Y., Lehrer, E. On some families of cooperative fuzzy games. Int J Game Theory 36, 1–15 (2007). https://doi.org/10.1007/s00182-007-0093-2
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DOI: https://doi.org/10.1007/s00182-007-0093-2