Theoretical Analysis of the VCG Mechanism for Sponsored Search Auctions by a Comprehensive Utility
38 Pages Posted: 6 Sep 2015
Date Written: September 6, 2015
Abstract
We investigate the VCG mechanism to which the locally envy-free Nash equilibria (LEFNE), vindictive bidding, and retaliating are applied. In order to evaluate performances of different bidding strategies with which an advertiser will acquire the same position, we define a novel so-called comprehensive utility (CU) by using both the advertiser’s own and other advertisers’ utility. The equilibrium we have found within all the LEFNEs in the sense of CU-maximization (i) is a unique dominant strategy different from truth-telling; (ii) is best preferred by both the advertisers and the search engine; (iii) can be achieved in finite bidding rounds. Thus, truth-telling is no longer an equilibrium in the sense of CU-maximization. Actually, it is the worst LEFNE for both the advertisers and the search engine. Finally, we give an easily operated and practical method for implementing the unique equilibrium. The search engine can use this method to find the valuations of all the advertisers.
Keywords: VCG, sponsored search auction, comprehensive utility, truth telling
JEL Classification: D44, L86, M37
Suggested Citation: Suggested Citation