Theoretical Analysis of the Extension of VCG Equilibrium in Sponsored Search Auction

Abstract In the sponsored search auction, VCG and GSP have been compared by researchers from computer science and economics in the last few years. However, there have been some experiments not well consistent with the existing literatures. We proposed that an assumption could be refined, namely the dominant-strategy equilibrium is still the unique valid VCG equilibrium concept in the sponsored search auction scenario. In this paper, we explored an approach to extend the VCG equilibrium concept by applying locally envy free Nash equilibrium (LEFNE) from GSP. We achieved two main results by theoretical analysis, which are 1) efficiency is still guaranteed under LEFNE in VCG; 2) the range of revenue of VCG and GSP coincide with each other. Thus, our proposed extension is supported to be valid.