A Modular Approach to Roberts' Theorem

Authors:
Shahar Dobzinski;Noam Nisan
Affiliations:
The School of Computer Science and Engineering, The Hebrew University of Jerusalem,;The School of Computer Science and Engineering, The Hebrew University of Jerusalem, and Google Tel Aviv,
Venue:
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Year:
2009

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Abstract

Roberts' theorem from 1979 states that the only incentive compatible mechanisms over a full domain and range of at least 3 are weighted variants of the VCG mechanism termed affine maximizers. Roberts' proof is somewhat "magical" and we provide a new "modular" proof. We hope that this proof will help in future efforts to extend the theorem to non-full domains such as combinatorial auctions or scheduling.