Theoretical Analysis of the VCG Mechanism for Sponsored Search Auctions by a Comprehensive Utility

38 Pages Posted: 6 Sep 2015

See all articles by Dongfeng liu

Dongfeng liu

University of International Business and Economics (UIBE)

Shulin Liu

University of International Business and Economics - Department of Quantitative Economics

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

liu, Dongfeng and Liu, Shulin, Theoretical Analysis of the VCG Mechanism for Sponsored Search Auctions by a Comprehensive Utility (September 6, 2015). Available at SSRN: https://ssrn.com/abstract=2656720 or http://dx.doi.org/10.2139/ssrn.2656720

Dongfeng Liu

University of International Business and Economics (UIBE) ( email )

10, Huixin Dongjie
Changyang District
Beijing, Beijing 100029
China

Shulin Liu (Contact Author)

University of International Business and Economics - Department of Quantitative Economics ( email )

10 East Huixin Street
Chaoyang District
Beijing, 100029
China

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
49
Abstract Views
540
PlumX Metrics