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How to Sell Information Optimally: An Algorithmic Study

Authors Yang Cai , Grigoris Velegkas

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Author Details

Yang Cai
  • Yale University, New Haven, CT, USA
Grigoris Velegkas
  • Yale University, New Haven, CT, USA

Funding

  • Cai, Yang: Supported by a Sloan Foundation Research Fellowship and the NSF Award CCF-1942583 (CAREER).
  • Velegkas, Grigoris: Partially supported by a PhD Scholarship from the Onassis Foundation and a PhD Scholarship from the Bodossaki Foundation.

Acknowledgements

We would like to thank Dirk Bergemann for helpful discussions and the anonymous reviewers for their valuable comments and suggestions.

Cite AsGet BibTex

Yang Cai and Grigoris Velegkas. How to Sell Information Optimally: An Algorithmic Study. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 81:1-81:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ITCS.2021.81

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. [Bergemann et al., 2018], 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. [Bergemann et al., 2018] that allows multiple agents to compete for useful information. We leverage techniques developed in the study of auction design (see e.g. [Yang Cai et al., 2012; Saeed Alaei et al., 2012; Yang Cai et al., 2012; Yang Cai et al., 2013; Yang Cai et al., 2013]) to design a polynomial time algorithm that computes the revenue-optimal mechanism for selling information.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Mechanism Design
  • Algorithmic Game Theory
  • Information Design

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