×

zbMATH — the first resource for mathematics

On the Shapley-Scarf economy: The case of multiple types of indivisible goods. (English) Zbl 1007.91036
From the authors’ summary: We study a generalization of Shapley-Scarf’s economy in which multiple types of indivisible goods are traded. We show that many of the distinctive results from the Shapley-Scarf economy do not carry over to this model… The core may be empty. The strict core, if nonempty, may be multi-valued, and might not coincide with the set of competitive allocations. Furthermore, there is no Pareto efficient, individually rational, and strategy-proof social choice rule.

MSC:
91B60 Trade models
91A40 Other game-theoretic models
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Le Breton, M; Sen, A, Separable preferences, Strategy proofness and decomposability. econometrica, 67, 605-628, (1999) · Zbl 1022.91020
[2] Ma, J, Strategy-proofness and the strict core in a market with indivisibilities, International journal of game theory, 23, 75-83, (1994) · Zbl 0804.90014
[3] Miyagawa, E., 1997. Strategy-proofness for the reallocation of multiple types of indivisible goods. Discussion paper, University of Rochester.
[4] Moulin, H., 1995. Cooperative Microeconomics. Princeton University Press, Princeton, NJ.
[5] Quint, T, Restricted houseswapping games, Journal of mathematical economics, 27, 451-470, (1997) · Zbl 0880.90145
[6] Roth, A, Incentive compatibility in a market with indivisibilities, Economics letter, 9, 127-132, (1982) · Zbl 0722.90009
[7] Roth, A; Postlewaite, A, Weak versus strong domination in a market with indivisible goods, Journal of mathematical economics, 4, 131-137, (1977) · Zbl 0368.90025
[8] Scarf, H, The core of an N-person game, Econometrica, 35, 50-69, (1967) · Zbl 0183.24003
[9] Shapley, L; Scarf, H, On cores and indivisibility, Journal of mathematical economics, 1, 23-37, (1974) · Zbl 0281.90014
[10] Sönmez, T, Implementation in generalized matching problems, Journal of mathematical economics, 26, 429-439, (1996) · Zbl 0876.90012
[11] Sönmez, T, Strategy-proofness and essentially single-valued cores, Econometrica, 67, 677-689, (1999) · Zbl 1021.91036
[12] Wako, J, A note on the strong core of a market with indivisible goods, Journal of mathematical economics, 13, 189-194, (1984) · Zbl 0563.90013
[13] Wako, J, Some properties of weak domination in an exchange market with indivisible goods, Economic studies quarterly, 42, 303-314, (1991)
[14] Wako, J., 1997. Coalition-proof Nash allocation in a barter game with multiple indivisible goods. Discussion paper, Gakushuin University, Tokyo. · Zbl 1127.91021
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.