No abstract

Position auctions were widely used by search engines to sell keyword advertising before being well understood (and, indeed, studied) theoretically. To date, theorists have made significant progress, for example showing that a given auction is efficient or revenue-dominates a benchmark auction such as VCG. This paper augments that line of work, relying on computational equilibrium analysis. By computing Nash equilibria and calculating their expected revenue and social welfare, we can quantitatively answer questions that theoretical methods have not. Broadly, the questions we answer are: (1) How often do the theoretically predicted "good" (i.e., efficient, high-revenue) equilibria of GSP occur? (2) In models where GSP is known to be inefficient, how much welfare does it waste? We also use our data to examine the larger question of whether GSP is a good choice, compared with the alternatives.

We consider the optimization of revenue in advertising auctions based on the generalized second-price (GSP) paradigm, which has become a de facto standard. We examine several different GSP variants (including squashing and different types of reserve prices), and consider how to set their parameters optimally. One intriguing finding is that charging each advertiser the same per-click reserve price ("unweighted reserve prices") yields dramatically more revenue than the quality-weighted reserve prices that have become common practice. This result is robust, arising both from theoretical analysis and from two different kinds of computational experiments. We also identify a new GSP variant that is revenue optimal in restricted settings. Finally, we study how squashing and reserve prices interact, and how equilibrium selection affects the revenue of GSP when features such as reserves or squashing are applied.

We consider the optimization of revenue in advertising auctions based on the generalized second-price (GSP) paradigm, which has become a de facto standard. We examine several different GSP variants (including squashing and different types of reserve prices), and consider how to set their parameters optimally. One intriguing finding is that charging each advertiser the same per-click reserve price ("unweighted reserve prices") yields dramatically more revenue than the quality-weighted reserve prices that have become common practice. This result is robust, arising both from theoretical analysis and from two different kinds of computational experiments. We also identify a new GSP variant that is revenue optimal in restricted settings. Finally, we study how squashing and reserve prices interact, and how equilibrium selection affects the revenue of GSP when features such as reserves or squashing are applied.

Abstract. The support-enumeration method (SEM) for computation of Nash equilibrium has been shown to achieve state-of-the-art empirical performance on normal-form games. Action-graph games (AGGs) are exponentially smaller than the normal form on many important classes of games. We show how SEM can be extended to the AGG representation, yielding an exponential improvement in worst-case runtime. Empirically, we demonstrate that our AGG-optimized SEM algorithm substantially outperforms the original SEM, and also outperforms state-of-the-art AGG-optimized algorithms on most problem distributions.