Equilibria in Auctions With Ad Types

TL;DR

This paper analyzes equilibrium qualities and efficiency bounds of semi-separable position auctions with various allocation and pricing rules, providing theoretical bounds, equilibrium characterizations, and empirical evaluations using real bidding data.

Contribution

It offers new bounds on the Price of Anarchy, characterizes Bayes-Nash equilibria in simple auction settings, and evaluates mechanism performance with real-world data.

Findings

Empirical welfare ratios outperform theoretical bounds.

Revenue hierarchies vary with valuation distributions.

Equilibrium characterizations hold across auction formats.

Abstract

This paper studies equilibrium quality of semi-separable position auctions (known as the Ad Types setting) with greedy or optimal allocation combined with generalized second-price (GSP) or Vickrey-Clarke-Groves (VCG) pricing. We make three contributions: first, we give upper and lower bounds on the Price of Anarchy (PoA) for auctions which use greedy allocation with GSP pricing, greedy allocations with VCG pricing, and optimal allocation with GSP pricing. Second, we give Bayes-Nash equilibrium characterizations for two-player, two-slot instances (for all auction formats) and show that there exists both a revenue hierarchy and revenue equivalence across some formats. Finally, we use no-regret learning algorithms and bidding data from a large online advertising platform and no-regret learning algorithms to evaluate the performance of the mechanisms under semi-realistic conditions. For welfare, we find that the optimal-to-realized welfare ratio (an empirical PoA analogue) is broadly better than our upper bounds on PoA; For revenue, we find that the hierarchy in practice may sometimes agree with simple theory, but generally appears sensitive to the underlying distribution of bidder valuations.