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Almost Quasi-linear Utilities in Disguise Positive-representation An Extension of Roberts Theorem

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Document pages: 21 pages

Abstract: This work deals with the implementation of social choice rules using dominantstrategies for unrestricted preferences. The seminal Gibbard-Satterthwaitetheorem shows that only few unappealing social choice rules can be implementedunless we assume some restrictions on the preferences or allow monetarytransfers. When monetary transfers are allowed and quasi-linear utilitiesw.r.t. money are assumed, Vickrey-Clarke-Groves (VCG) mechanisms were shown toimplement any affine-maximizer, and by the work of Roberts, onlyaffine-maximizers can be implemented whenever the type sets of the agents arerich enough.In this work, we generalize these results and define a new class ofpreferences: Preferences which are positive-represented by a quasi-linearutility. That is, agents whose preference on a subspace of the outcomes can bemodeled using a quasi-linear utility. We show that the characterization of VCGmechanisms as the incentive-compatible mechanisms extends naturally to thisdomain. Our result follows from a simple reduction to the characterization ofVCG mechanisms. Hence, we see our result more as a fuller more correct versionof the VCG characterization.This work also highlights a common misconception in the community attributingthe VCG result to the usage of transferable utility. Our result shows that theincentive-compatibility of the VCG mechanisms does not rely on money being acommon denominator, but rather on the ability of the designer to fine theagents on a continuous (maybe agent-specific) scale.We think these two insights, considering the utility as a representation andnot as the preference itself (which is common in the economic community) andconsidering utilities which represent the preference only for the relevantdomain, would turn out to fruitful in other domains as well.

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