When Bribes are Harmless: The Power and Limits of Collusion-Resilient Mechanism Design

26 Pages Posted: 27 Feb 2018 Last revised: 10 May 2019

See all articles by Artur Gorokh

Artur Gorokh

Cornell University - Center for Applied Mathematics

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering

Krishnamurthy Iyer

University of Minnesota - Twin Cities - Department of Industrial and Systems Engineering

Date Written: May 08, 2019

Abstract

Collusion has long been the Achilles heel of mechanism design, as most results break down when participating agents can collude. The issue is more severe when monetary transfers (bribes) between agents are feasible, wherein it is known that truthful revelation and efficient allocation are incompatible. A natural relaxation that circumvents these impossibility results is that of coalitional dominance: replacing truthful revelation with the weaker requirement that all coalitions, whatever they may be, have dominant strategies. When a mechanism satisfies this property and is efficient, we call it collusion resilient. The goal of this paper is to characterize the power and limits of collusion resilient mechanisms.

On the positive side, in a general allocation setting, we demonstrate a new mechanism which is collusion-resilient for surplus-submodular settings -- a large-class of problems which includes combinatorial auctions with gross substitutes valuations. We complement this mechanism with two impossibility results: (1) for combinatorial auctions with general submodular valuations, we show that no mechanism can be collusion-resilient, and (2) for the problem of collective decision making, we argue that any non-trivial approximation of welfare is impossible under coalitional dominance. Finally, we make a connection between collusion resilience and false-name-proofness, and show that our impossibility theorems strengthen existing results for false-name-proof mechanisms.

Keywords: mechanism design, collusion, efficient allocation, impossibility results, surplus submodularity

JEL Classification: C70, D70

Suggested Citation

Gorokh, Artur and Banerjee, Siddhartha and Iyer, Krishnamurthy, When Bribes are Harmless: The Power and Limits of Collusion-Resilient Mechanism Design (May 08, 2019). Available at SSRN: https://ssrn.com/abstract=3125003 or http://dx.doi.org/10.2139/ssrn.3125003

Artur Gorokh (Contact Author)

Cornell University - Center for Applied Mathematics ( email )

657 Rhodes Hall
Ithaca, NY 14853-3801
United States

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

Krishnamurthy Iyer

University of Minnesota - Twin Cities - Department of Industrial and Systems Engineering ( email )

111 Church St SE
Minneapolis, MN 55455
United States

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