Chapter

Algorithmic Game Theory

Volume 5814 of the series Lecture Notes in Computer Science pp 14-23

A Modular Approach to Roberts’ Theorem

  • Shahar DobzinskiAffiliated withThe School of Computer Science and Engineering, The Hebrew University of Jerusalem
  • , Noam NisanAffiliated withThe School of Computer Science and Engineering, The Hebrew University of JerusalemGoogle Tel Aviv

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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.