zbMATH — the first resource for mathematics

Large cores and exactness. (English) Zbl 0957.91009
The authors answers that every exact game has a large core for 3 or 4-person games and the statement does not hold for games with 5 or more players. They also show that a large core, a stable core and exactness are equivalent for totally balanced symmetric games.

91A12 Cooperative games
Full Text: DOI
[1] Biswas, A. K, Ravindran, G, and, Parthasarathy, T. 1996, Stability and Largeness of the Core of Symmetric Games, Technical Report no, 31, Statistical Quality Control & Operations Research Unit, ISI Madras. · Zbl 0944.91002
[2] Bondareva, O., Certain applications of the methods of linear programming to the theory of cooperative games, Problemy kibernetiki, 10, 119-139, (1963) · Zbl 1013.91501
[3] Gellekom, A. van, Potters, J. A. M, and, Reijnierse, J. H. 1998, Prosperty properties for TU-games, Discussion Paper No. 9811 of the, Mathematical Institute KUN, Nijmegen, The Netherlands. · Zbl 0941.91008
[4] Kikuta, K., A condition for a game to be convex, Math. japonica, 33, 425-430, (1988) · Zbl 0658.90108
[5] Kulakovskaja, T.E., The solution of a class of cooperative four-person games with nonempty core, Vestnik leningrad univ. math., 12, 286-292, (1980) · Zbl 0437.90106
[6] Lucas, W.F., Some recent developments in n-person game theory, SIAM rev., 13, 491-523, (1969) · Zbl 0229.90055
[7] Moulin, H., Cores and large cores when population varies, Int. J. game theory, 19, 219-232, (1990) · Zbl 0715.90102
[8] Schmeidler, D., Cores of exact games, J. math. anal. appl., 40, 214-225, (1972) · Zbl 0243.90071
[9] Shapley, L.S., On balanced sets and cores, Naval res. logistic Q, 14, 453-460, (1967)
[10] Shapley, L. S. 1974, Core stability in symmetric games, Mimeo.
[11] Shapley, L. S, and, Kikuta, K. 1986, Core stability in n-person games, Mimeo.
[12] Sharkey, W.W., Cooperative games with large cores, Int. J. game theory, 11, 175-182, (1982) · Zbl 0494.90096
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.