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Social Choice and Welfare

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01-02-2015

Mechanism design with two alternatives in quasi-linear environments

Authors: Thierry Marchant, Debasis Mishra

Published in: Social Choice and Welfare | Issue 2/2015

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Abstract

We study mechanism design in quasi-linear private values environments when there are two alternatives. We show that under a mild range condition, every implementable allocation rule is a generalized utility function maximizer. In unbounded domains, if we replace our range condition by an independence condition, then every implementable allocation rule is an affine maximizer. Our results extend Roberts’ affine maximizer theorem (Roberts, In: Laffont J-J (ed) The characterization of implementable choice rules, 1979) to the case of two alternatives.

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Most of our results require some richness of the domain. We discuss these specifics of the domain restrictions later in the paper.

Unanimity requires that if valuation of every agent for an alternative is larger than the other alternative, then the higher valuation alternative must be the outcome of the allocation rule. Transitivity requires that outcomes at three valuation profiles which are linked in a certain way must be transitive in some sense.

What we call agent sovereignty, Lavi et al. (2009) refer to it as player decisiveness.

To remind, \(D_i = \{\partial v_i: v_i \in V_i\}\).

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Title: Mechanism design with two alternatives in quasi-linear environments
Authors: Thierry Marchant
Debasis Mishra
Publication date: 01-02-2015
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 2/2015
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-014-0837-4

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