Learning Prices for Repeated Auctions with Strategic Buyers

TL;DR

This paper studies how sellers can learn optimal prices in repeated auctions with strategic buyers, proposing algorithms that minimize revenue loss under certain buyer discounting assumptions.

Contribution

It introduces seller algorithms that achieve no-regret learning in repeated posted-price auctions with strategic buyers, and establishes lower bounds on regret based on buyer discounting.

Findings

Seller algorithms achieve no-regret when buyers heavily discount future surplus.

Lower bounds show regret increases as buyers discount less, becoming linear with no discounting.

The results inform pricing strategies in online ad exchanges with strategic participants.

Abstract

Inspired by real-time ad exchanges for online display advertising, we consider the problem of inferring a buyer's value distribution for a good when the buyer is repeatedly interacting with a seller through a posted-price mechanism. We model the buyer as a strategic agent, whose goal is to maximize her long-term surplus, and we are interested in mechanisms that maximize the seller's long-term revenue. We define the natural notion of strategic regret --- the lost revenue as measured against a truthful (non-strategic) buyer. We present seller algorithms that are no-(strategic)-regret when the buyer discounts her future surplus --- i.e. the buyer prefers showing advertisements to users sooner rather than later. We also give a lower bound on strategic regret that increases as the buyer's discounting weakens and shows, in particular, that any seller algorithm will suffer linear strategic regret if there is no discounting.