# How to Sell Information Optimally: an Algorithmic Study

arXiv: https://arxiv.org/abs/2011.14570 · HTML: https://mlsanity.com/paper/2011.14570/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [Data Market Design through Deep Learning](https://mlsanity.com/paper/2310.20096/) (2023)
- [Equilibrium of Data Markets with Externality](https://mlsanity.com/paper/2302.08012/) (2023)
- [Modelling Opaque Bilateral Market Dynamics in Financial Trading: Insights from a Multi-Agent Simulation Study](https://mlsanity.com/paper/2405.02849/) (2024)
- [How to Sell High-Dimensional Data Optimally](https://mlsanity.com/paper/2510.15214/) (2025)
- [Learning to Price with Persuasion](https://mlsanity.com/paper/2608.16699/) (2026)

## Abstract (arXiv)

We investigate the algorithmic problem of selling information to agents who face a decision-making problem under uncertainty. We adopt the model recently proposed by Bergemann et al. [BBS18], in which information is revealed through signaling schemes called experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. Our results show that the computational complexity of designing the revenue-optimal menu depends heavily on the way the model is specified. When all the parameters of the problem are given explicitly, we provide a polynomial time algorithm that computes the revenue-optimal menu. For cases where the model is specified with a succinct implicit description, we show that the tractability of the problem is tightly related to the efficient implementation of a Best Response Oracle: when it can be implemented efficiently, we provide an additive FPTAS whose running time is independent of the number of actions. On the other hand, we provide a family of problems, where it is computationally intractable to construct a best response oracle, and we show that it is NP-hard to get even a constant fraction of the optimal revenue. Moreover, we investigate a generalization of the original model by Bergemann et al. [BBS18] that allows multiple agents to compete for useful information. We leverage techniques developed in the study of auction design (see e.g. [CDW12a], [AFHHM12], [CDW12b], [CDW13a], [CDW13b]) to design a polynomial time algorithm that computes the revenue-optimal mechanism for selling information.