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How to Sell Information Optimally: An Algorithmic Study

Authors Yang Cai , Grigoris Velegkas

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

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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.

Cite As Get 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

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.

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