How to Sell Information Optimally: an Algorithmic Study

TL;DR

This paper studies the computational aspects of selling information optimally through signaling schemes, providing algorithms for different model specifications and extending to multi-agent scenarios with competitive settings.

Contribution

It offers polynomial algorithms for explicit models, an FPTAS for succinct models with efficient best response oracles, and proves NP-hardness in intractable cases, also extending to multi-agent settings.

Findings

Polynomial time algorithm for explicit models

Additive FPTAS for succinct models with efficient oracles

NP-hardness results for intractable cases

Abstract

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.