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DOI: 10.4230/LIPIcs.ITCS.2021.81
How to Sell Information Optimally: An Algorithmic Study

Authors: Yang Cai and Grigoris Velegkas

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

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

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)

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@InProceedings{cai_et_al:LIPIcs.ITCS.2021.81,
  author =	{Cai, Yang and Velegkas, Grigoris},
  title =	{{How to Sell Information Optimally: An Algorithmic Study}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{81:1--81:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.81},
  URN =		{urn:nbn:de:0030-drops-136205},
  doi =		{10.4230/LIPIcs.ITCS.2021.81},
  annote =	{Keywords: Mechanism Design, Algorithmic Game Theory, Information Design}
}
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