Generalized second price auctions with value externalities

We consider a new setting of ad auctions with value externalities. Under such a setting, we perform theoretic analysis on two implementations of generalized second price auctions (GSP): GSPS and GSPV. Our analysis shows that both GSPS and GSPV admit at least one pure Nash equilibrium for the single-slot case, while pure Nash equilibrium may not exist for the multi-slot case. Furthermore, we prove that the price of anarchy of GSPS does not have a constant upper bound, while for GSPV one can achieve a constant upper bound under mild assumptions.