Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions

In analyses of sponsored search auctions for online advertising, it is customary to model the dynamic game of incomplete information by considering a static games of complete information. This approach is used in Edelman, Ostrovsky and Schwarz (2007) (EOS), Varian (2007), and the subsequent literature. Modeling complex interactions in uncertain environments as games of complete information has a long history. For example, the Bertrand model of oligopolistic competition posits that companies know their competitors’ costs based on their experience from prior interactions. The use of a static game of complete information often offers important benefits. For one, it is tractable – avoiding complex multi-period information sets in a dynamic game. Furthermore, a suitably-chosen static game can capture important characteristics of the underlying dynamic game. When a game is repeated over an extended period, there is good reason to think participants will learn many characteristics of their counterparts – supporting the use of a complete information model. Yet the use of a static game of complete information is also unsatisfying. There is no clear way to identify which (if any) equilibria of the static game of complete information are a relevant approximation of the equilibria of the dynamic game of incomplete information. In this paper, we consider a dynamic game of incomplete information used to sell sponsored