Abstract
We consider the assignment game of Shapley and Shubik (1972). We prove that the class of possible cores of such games (expressed in terms of payoffs for players on one side of the market) is exactly the same as a special class of polytopes, called “45‡-lattices”. These results parallel similar work done by Conway (in Knuth, 1976) and Blair (1984) for marriage markets.
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Balinski ML, Gale D (1988) On the Core of the Assignment Game, working paper, Laboratoire D'Econometrie, Ecole Polytechnique, Paris, France
Blair C (1984) Every Finite Distributive Lattice is a Set of Stable Matchings, Journal of Combinatorial Theory, Series A, 37, pp. 353–356
Gale D, Shapley L (1962) College Admissions and the Stability of Marriage, American Mathematical Monthly, 69, pp. 9–15
Knuth D (1976) Mariages Stables, Montreal University Press, pp. 87–92
Shapley L, Shubik M (1972) The Assignment Game I: The Core, International Journal of Game Theory, 1, pp. 111–130
Thompson, GL (1980) Computing the Core of a Market Game, in Fiacco AV, Kortanek KO (eds.), Extremal Methods and Systems Analysis, Lecture Notes in Economics and Mathematical Systems 174, Springer-Verlag, pp. 312–324
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Research supported by the Office of Naval Technology.
The author wishes to thank an anonymous referee for a shortened proof to the paper's Lemma.
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Quint, T. Characterization of cores of assignment games. Int J Game Theory 19, 413–420 (1991). https://doi.org/10.1007/BF01766430
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DOI: https://doi.org/10.1007/BF01766430