On the Shapley-Scarf economy: The case of multiple types of indivisible goods.

*(English)*Zbl 1007.91036From 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.

Reviewer: Albrecht Irle (Kiel)

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\textit{H. Konishi} et al., J. Math. Econ. 35, No. 1, 1--15 (2001; Zbl 1007.91036)

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##### 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 |

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