Is Selling Complete Information (Approximately) Optimal?

02/18/2022
by   Dirk Bergemann, et al.
0

We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by [Blackwell, 1951, 1953]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. [Bergemann et al., 2018] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m≥ 3 actions, we provide an O(m)-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.

READ FULL TEXT

Authors

page 12

page 30

page 31

page 32

03/09/2021

Selling Data to an Agent with Endogenous Information

We consider the model of the data broker selling information to a single...
11/30/2020

How to Sell Information Optimally: an Algorithmic Study

We investigate the algorithmic problem of selling information to agents ...
02/24/2020

Optimal Advertising for Information Products

When selling information, sometimes the seller can increase the revenue ...
11/06/2017

The menu complexity of "one-and-a-half-dimensional" mechanism design

We study the menu complexity of optimal and approximately-optimal auctio...
08/29/2017

Bounding the Menu-Size of Approximately Optimal Auctions via Optimal-Transport Duality

The question of the minimum menu-size for approximate (i.e., up-to-ε) Ba...
06/02/2020

Hierarchical Clustering: a 0.585 Revenue Approximation

Hierarchical Clustering trees have been widely accepted as a useful form...
01/24/2022

Public Signaling in Bayesian Ad Auctions

We study signaling in Bayesian ad auctions, in which bidders' valuations...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.