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General Matching: Lattice Structure of the Set of Agreements

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  • Aron Matskin
  • Daniel Lehmann

Abstract

The subset agreement problem generalizes all forms of two-sided matching. Two agents need to agree on some subset of a given finite set of contracts. A solution concept - agreement - generalizes the notion of a stable subset. Its definition does not require the consideration of a preference ordering on sets of contracts, but only that of the choice function that reveals the agents' preferences by choosing the best subset of any given set of contracts. Under a suitable condition, called coherence, that requires that contracts are substitutes to one another, at least one greement always exists. A constructive proof is given that the structure of the set of agreements is a lattice.

Suggested Citation

  • Aron Matskin & Daniel Lehmann, 2009. "General Matching: Lattice Structure of the Set of Agreements," Discussion Paper Series dp501, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp501
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    References listed on IDEAS

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