Bayes-Nash Equilibria in Generalized Second Price Auctions with Allocative Externalities

Abstract

In this paper, we investigate an incomplete information model of generalized second price auctions with allocative externalities originating from the heterogeneous match rates of bidders. A novel feature of our model is that it generates endogenous click-through rates (CTRs). In this setting, we establish existence of symmetric efficient equilibria for common classes of primitives. This contrasts with the findings of Gomes and Sweeney (2014), who study a similar model but with fixed CTRs. Moreover, nonexistence results require strong assumptions on the primitives of the model. We conclude that existence of equilibria in GSP with incomplete information is quite general.

Mixed Mechanisms for Auctioning Ranked Items

“…However, they provide conditions under which this equilibrium exists. Lu and Riis [50] complement the analysis of Gomes and Sweeney [6] by considering allocative externalities arising from the heterogeneous match rates of bidders, obtaining similar results concerning the existence of a Bayesian Nash equilibrium. In addition, applications of the GSP to other fields different than sponsored keywords markets can be found in the literature, see for example, Reference [7] or Reference [51].…”