Equilibrium Selection, Inefficiency, and Instability in Internet Advertising Auctions

Abstract

This paper studies a model in which a non-strategic bidder named the noise bidder secretly participate in the generalized second price auction with a small probability. The main result is that the VCG equilibrium, which have been considered as the most plausible equilibrium in this literature, is no longer an equilibrium even in the limit where the noise bidder disappears. In this game, an efficient equilibrium is unique if exists. This unique equilibrium is further justified as a unique limit of trembling-hand perfect equilibria in which all bidders mistake in similar ways. However, this game may not have any efficient equilibrium, or more seriously any stable equilibrium. A simulation result suggests that in the parameter space the set of parameters such that no stable equilibrium exists is huge. It occupies more than 95% of the space if five or more positions are traded.

Keywords: Generalized second price auction; Position auctions; Online advertising; Equilibrium selection

JEL Classification: D44; L86; M37