Abstract
The discussion will center mainly on some work on two solution concepts: the core for gaines without side payments and the nucleolus for games with side payments (characteristic funtion games). The core has become an important equilibrium concept in mathematical economics. The nucleolus is related to the theory of bargaining sets.
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References
L.J.Billera, “Some theorems on the core of ann-person game without side payments”,SIAM Journal of Applied Mathematics 18 (1970) 567–579.
O.N.Bondareva, “Some applications of linear programming methods to the theory of cooperative games”,Problemy Kibernet. 10 (1963) 119–139.
A.Charnes, M.Eisner and K.O.Kortanek, “On weakly balanced games and duality theory”,Cahiers du Centre D'Etudes De Recherche Opérationelle 12 (1970) 7–21.
A.Charnes and K.Kortanek, “On classes of convex and preemptive nuclei forn-person games”,Proc. 1967 Princeton Mathematical Programming Symposium, ed. H.W. Kuhn (Princeton University Press, Princeton, 1970) pp. 377–390.
A.Charnes and K.Kortanek, “On asymptotic behavior of some nuclei ofn-person games and the piecewise linearity of the nucleolus”, Management Science Research Report No. 170, Carnegie-Mellon University (August, 1969).
M.Eisner, “On duality in infinite-player games and sequential chance-constrained programming”, Ph. D. thesis, Department of Operations Research, Cornell University (January, 1970).
J.Grotte, “Computation of and observations on the nucleolus, the normalized nucleolus, and the central games”, M.S. thesis, Field of Applied Mathematics, Cornell University (September, 1970).
Y. Kannai, “Countably additive measures in cores of games”,Journ. Math. Anal. and Applic. 27 (1969) 227–240.
M.Keane, “Some topics inn-person game theory”, Ph.D. thesis, Northwestern University (June, 1969).
E.Kohlberg, “On the nucleolus of a characteristic function game”, Research memorandum No. 48, Department of Mathematics, The Hebrew University of Jerusalem (July, 1969). (To appear inSIAM Journal of Applied Mathematics).
E.Kohlberg, “The nucleolus as a solution of a minimization problem”, to appear.
A.Kopelowitz, “Computation of the kernels of simpel games and the nucleolus ofn-person games”, Research Memorandum No. 31, Department of Mathematics, The Hebrew University of Jerusalem (September, 1967).
M.Maschler, B.Peleg and L.S.Shapley, “The kernel and the nucleolus of a cooperative game as locuses in the strong∈-core”, Research Memorandum No. 60, Department of Mathematics, The Hebrew University of Jerusalem (May, 1970).
H.Scarf, “The core of ann-person game”,Econometrica 35 (1967) 50–69.
D. Schmeidler, “The nucleolus of a characteristic funtion game”,SIAM Journal of Applied Mathematics 17 (1969) 1163–1170.
D.Schmeidler, “On balanced games with infinitely many players”, Research Memorandum No. 28, Department of Mathematics, The Hebrew University of Jerusalem (June, 1967).
L.Shapley, “On balanced sets and scores”.Naval Research Logistics Quarterly 14 (1967) 453–460.
L.Shapley, “Balanced sets, Sperner's lemma, and Scarf's theorem on the core”, informal lecture at the Second International Game Theory Workshop, Berkeley, August, 1970. To appear (RAND Corporation, Santa Monica, California).
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This work was supported by the National Science Foundation under grant GK-4795.
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Billera, L.J. Some recent results inn-person game theory. Mathematical Programming 1, 58–67 (1971). https://doi.org/10.1007/BF01584072
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DOI: https://doi.org/10.1007/BF01584072