Selling an Item Among a Strategic Bidder and a Profiled Agent

TL;DR

This paper designs and analyzes auction mechanisms for selling an item to two agents, one of whom is profiled with a predicted valuation, aiming to maximize revenue under prediction accuracy and distribution assumptions.

Contribution

It introduces two mechanisms that achieve near-optimal revenue guarantees in the presence of valuation predictions, under the monotone hazard rate distribution assumption.

Findings

The first mechanism is optimal with perfect predictions and approximates revenue when predictions are incorrect.

The second mechanism ignores predictions and still guarantees a constant revenue approximation.

The MHR distribution assumption is necessary; non-MHR distributions may not allow constant approximation.

Abstract

We consider the fundamental scenario where a single item is to be sold to one of two agents. Both agents draw their valuation for the item from the same probability distribution. However, only one of them submits a bid to the mechanism. The other agent is profiled, i.e., the mechanism receives a prediction for her valuation, which can be true or false. Our goal is to design mechanisms for selling the item that make as much revenue as possible in cases of a correct or incorrect prediction. As a benchmark for proving our revenue-approximation guarantees, we use the maximum expected revenue that can be obtained by a strategic and an honest bidder. We study two mechanisms. The first one yields optimal revenue when the prediction is guaranteed to be correct and a constant revenue approximation when the prediction is incorrect, assuming that the agent valuations are drawn from a monotone hazard rate (MHR) distribution. The second mechanism ignores the prediction for the second agent and simulates the revenue-optimal mechanism when no bid information for the bidders is available. We prove, again assuming that valuations are drawn from MHR distributions, that this mechanism achieves a constant revenue approximation guarantee compared to our revenue benchmark. The MHR assumption is necessary; we show that there are non-MHR but regular probability distributions for which no constant approximation of our revenue benchmark is possible.