On strategy-proofness and essentially single-valued cores: A converse result

Koji Takamiya ()
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Koji Takamiya: Graduate School of Economics and Business Administration, Hokkaido University, Kita9 Nishi7 Sapporo 060-0809 Japan

Social Choice and Welfare, 2003, vol. 20, issue 1, 77-83

Abstract: In a general model of indivisible good allocation, Sönmez (1999) established that, whenever the core is nonempty for each preference profile, if an allocation rule is strategy-proof, individually rational and Pareto optimal, then the rule is a selection from the core correspondence, and the core correspondence must be essentially single-valued. This paper studies the converse claim of this result. I demonstrate that whenever the preference domain satisfies a certain condition of `richness', if the core correspondence is essentially single-valued, then any selection from the core correspondence is strategy-proof (even weakly coalition strategy-proof, in fact). In particular, on the domain of preferences in which each individual has strict preferences over his own assignments and there is no consumption externality, such an allocation rule is coalition strategy-proof. And on this domain, coalition strategy-proofness is equivalent to Maskin monotonicity, an important property in implementation theory.

Date: 2003-01-13
Note: Received: 22 February 2000/Accepted: 22 January 2002
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