Meta Research

This paper studies equilibrium quality of semi-separable position auctions (known as the Ad Types setting [9]) 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 allocation 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 to evaluate the performance of the mechanisms under semi-realistic conditions. We find that the VCG mechanism tends to obtain revenue and welfare comparable to or better than that of the other mechanisms. We also find that in practice, each of the mechanisms obtains significantly better welfare than our worst-case bounds might suggest.