Optimal Mechanisms for Selling Information

TL;DR

This paper investigates the design of optimal selling mechanisms for information in online marketplaces, providing conditions for simple protocols, algorithms for their computation, and insights into the necessity of multi-round disclosures.

Contribution

It introduces a framework for optimal information selling mechanisms, identifies when simple protocols suffice, and explores the complexity of multi-round disclosure strategies.

Findings

Single-round protocols can be optimal under certain conditions.

A polynomial-time algorithm computes the optimal mechanism.

Multi-round disclosures may be necessary for optimal revenue.

Abstract

The buying and selling of information is taking place at a scale unprecedented in the history of commerce, thanks to the formation of online marketplaces for user data. Data providing agencies sell user information to advertisers to allow them to match ads to viewers more effectively. In this paper we study the design of optimal mechanisms for a monopolistic data provider to sell information to a buyer, in a model where both parties have (possibly correlated) private signals about a state of the world, and the buyer uses information learned from the seller, along with his own signal, to choose an action (e.g., displaying an ad) whose payoff depends on the state of the world. We provide sufficient conditions under which there is a simple one-round protocol (i.e. a protocol where the buyer and seller each sends a single message, and there is a single money transfer) achieving optimal revenue. In these cases we present a polynomial-time algorithm that computes the optimal mechanism. Intriguingly, we show that multiple rounds of partial information disclosure (interleaved by payment to the seller) are sometimes necessary to achieve optimal revenue if the buyer is allowed to abort his interaction with the seller prematurely. We also prove some negative results about the inability of simple mechanisms for selling information to approximate more complicated ones in the worst case.