2023 Theses Doctoral

Bayesian Auction Design and Approximation

Jin, Yaonan

We study two classes of problems within Algorithmic Economics: revenue guarantees of simple mechanisms, and social welfare guarantees of auctions. We develop new structural and algorithmic tools for addressing these problems, and obtain the following results:

In the 𝑘-unit model, four canonical mechanisms can be classified as: (i) the discriminating group, including Myerson Auction and Sequential Posted-Pricing, and (ii) the anonymous group, including Anonymous Reserve and Anonymous Pricing. We prove that any two mechanisms from the same group have an asymptotically tight revenue gap of 1 + θ(1 /√𝑘), while any two mechanisms from the different groups have an asymptotically tight revenue gap of θ(log 𝑘).

In the single-item model, we prove a nearly-tight sample complexity of Anonymous Reserve for every value distribution family investigated in the literature: [0, 1]-bounded, [1, 𝐻]-bounded, regular, and monotone hazard rate (MHR).

Remarkably, the setting-specific sample complexity poly(𝜖⁻¹) depends on the precision 𝜖 ∈ (0, 1), but not on the number of bidders 𝑛 ≥ 1. Further, in the two bounded-support settings, our algorithm allows correlated value distributions. These are in sharp contrast to the previous (nearly-tight) sample complexity results on Myerson Auction.

In the single-item model, we prove that the tight Price of Anarchy/Stability for First Price Auctions are both PoA = PoS = 1 - 1/𝜖² ≈ 0.8647.