User data in auctions

Abstract

We study several optimization problems in algorithmic game theory. More concretely, we study auctions, design mechanisms between the seller and the buyers, and then provide theoretical analysis for performances.

The first problem in this thesis is the price discrimination problem introduced in \cite{bergemann2015limits} (Bergemann et al., 2015). In this problem, there is an intermediary between the buyer and the seller, and the intermediary can design market segments. The intermediary's goal is to maximize any linear combination of the buyer's utility and the seller's utility (revenue). While \cite{bergemann2015limits} assumed that the intermediary knows exactly the buyer's data, we study the case when the intermediary can only have partial information. In this work we consider three different models of information, and present algorithms to compute optimal or approximately optimal market segmentation.

The second problem in this thesis is the revenue maximization problem in one-item multi-buyer auctions. In most of classic models, the data of buyers can be learned via independent and identically distributed (i.i.d.) samples draw from some Bayesian prior. In this work we introduce targeted sampling model, which extends the model in \citet{chen2018brief}. The learner is allowed to draw samples with some specific quantiles, instead of the i.i.d. sampling. We design algorithms and prove that in this model the number of samples needed is strictly decreased, compared to the classic i.i.d. model.