## Abstract

Let (R_{1},...,R_{k}) be an arbitrary partition of the grand coalition in an atomless exchange economy with k "large enough." We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R_{i}'s. K is "large enough" if k ≥ r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ≤ n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).

Original language | English |
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Pages (from-to) | 166-171 |

Number of pages | 6 |

Journal | Journal of Economic Theory |

Volume | 35 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1985 |

### Bibliographical note

Funding Information:work was initiated when the authors were fellows of the Institute The Hebrew University, Mount Scopus, Jerusalem. Israel. author gratefully acknowledges the support of the NSF under Grant SOC 79-08989. thank R. J. Aumann, J. Greenberg and D. Samet for valuable discussions.

## ASJC Scopus subject areas

- Economics and Econometrics