Learning Utilities and Equilibria in Non-Truthful Auctions

In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents suffice for an algorithm to learn the interim utilities for all monotone bidding strategies. As a consequence, this number of samples suffice for learning all approximate equilibria. We give almost matching (up to polylog factors) lower bound on the sample complexity for learning utilities. We also consider settings where agents must pay a search cost to discover their own types. Drawing on a connection between this setting and the first price auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde O(n / \epsilon^2)$ samples suffice for utilities and equilibria to be estimated in a near welfare-optimal descending auction in this setting. En route, we improve the sample complexity bound, recently obtained by Guo et al. (2019), for the Pandora's Box problem, which is a classical model for sequential consumer search

Bayesian Auction Design and Approximation

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 -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 /√), while any two mechanisms from the different groups have an asymptotically tight revenue gap of θ(log ). 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, ]-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific sample complexity poly(⁻¹) depends on the precision ∈ (0, 1), but not on the number of bidders ≥ 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 - 1/² ≈ 0.8647