Cary, Matthew, Aparna Das, Benjamin Edelman, Ioannis Giotis, Kurtis Heimerl, Anna Karlin, Scott Duke Kominers, Claire Mathieu, and Michael Schwarz. “Convergence of Position Auctions under Myopic Best-Response Dynamics.” ACM Transactions on Economics and Computation 2, no. 3 (July 2014): 1-20.
We study the dynamics of multi-round position auctions, considering both the case of exogenous click-through rates and the case in which click-through rates are determined by an endogenous consumer search process. In both contexts, we demonstrate that the dynamic auctions converge to their associated static, envy-free equilibria. Furthermore, convergence is efficient, and the entry of low-quality advertisers does not slow convergence. Because our approach predominantly relies on assumptions common in the sponsored search literature, our results suggest that dynamic position auctions converge more generally.