Revenue maximization with incomplete information

Abstract

We study several revenue maximization scenarios in which each party holds asymmetric and incomplete information of the market. We design truthful mechanisms in each setting and provide theoretical analysis for their performances.

The first model we consider is selling a single item to a buyer, on whose private value the seller has a noisy signal. The value and the signal are drawn from a publicly known correlated distribution. The buyer knows her private value and the seller sees the signal. We study the optimal revenues when the signal is kept private or leaked. We prove that if the seller is not allowed to make payments to the buyer and the conditional distribution of value is regular for every signal, the gap between the two is bounded by $3$. Moreover, both conditions are necessary to admit a constant bound on the gap.

Recently, Carroll~(Econometrica 2017) proposed the correlation-robust framework to study the multi-item monopoly problem with a single buyer. Lu and Gravin~(SODA 2018) further extended the result to budget-constrained buyers. In the second part of this thesis, we adapt the framework to investigate the classic problem of selling a single item to multiple buyers. The auctioneer is assumed to have only partial information about the buyers' marginal distributions and aims at designing a mechanism that achieves the optimal worst-case revenue guarantee over the uncertainty of the joint value distribution. We prove that the best sequential posted prices mechanism achieves $4.78$ approximation to the optimal correlation-robust mechanism and is asymptotically optimal when all buyers have the same marginal distribution and the number of buyers goes to infinity.

Finally, we consider the online shopping scenario that customers have a large menu of options to choose from. However, most people do not browse the entire menu before making a decision. Motivated by such impatient behavior of the buyer, we consider the monopoly problem for a unit-demand buyer where the seller displays the menu dynamically page after a page to the buyer. The buyer incurs a cost for browsing through one menu page and stops whenever the cost exceeds the increase in her utility. We find simple and approximately optimal mechanisms with a bait structure, that use part of the items as a ``bait'' to attract the buyer with low prices, while at the same time showing expensive items to extract revenue.