Nontruthful Position Auctions Are More Robust to Misspecification

Author:

Dütting Paul1ORCID,Fischer Felix2ORCID,Parkes David C.3ORCID

Affiliation:

1. Google Research, Zurich 8002, Switzerland;

2. School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom;

3. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Boston, Massachusetts 02134

Abstract

We consider the classical model of sponsored search due to Edelman et al. and Varian and examine how robust standard position auctions are to a misspecification of the position-dependent quality factors used by this model. We show that under both complete and incomplete information a nontruthful position auction admits an efficient equilibrium for a strictly broader range of parameter values than the Vickrey-Clarke-Groves (VCG) mechanism, which would be truthful if the parameters were specified correctly. Our result for complete information concerns the generalized second-price (GSP) mechanism and is driven by a detailed understanding of the Nash equilibrium polytopes of the VCG mechanism and the GSP mechanism. Our result for incomplete information concerns the generalized first-price (GFP) mechanism and uses a surprising connection between the unique candidate equilibrium bidding functions of the VCG mechanism and the GFP mechanism. Funding: F. Fischer was supported by the Engineering and Physical Sciences Research Council [Grant EP/T015187/1] and Einstein Stiftung Berlin.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Management Science and Operations Research,Computer Science Applications,General Mathematics

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