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

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.

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.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} }

Document

**Published in:** LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Finite automata on infinite words (omega-automata) proved to be a powerful weapon for modeling and reasoning infinite behaviors of reactive systems. Complementation of omega-automata is crucial
in many of these applications. But the problem is non-trivial; even after extensive study during the past two decades, we still have an important type of omega-automata, namely Streett automata, for which the gap between the current best lower bound 2^(Omega(n lg nk)) and upper bound 2^(O (nk lg nk)) is substantial, for the Streett index size k can be exponential in the number of states n. In a previous work we showed a construction for complementing Streett automata with the upper bound 2^(O(n lg n+nk lg k)) for k = O(n) and 2^(O(n^2 lg n)) for k = omega(n). In this paper we establish a matching lower bound 2^(Omega (n lg n+nk lg k)) for k = O(n) and 2^(Omega
(n^2 lg n)) for k = omega(n), and therefore showing that the construction is asymptotically optimal with respect to the ^(Theta(.)) notation.

Yang Cai and Ting Zhang. A Tight Lower Bound for Streett Complementation. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 339-350, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{cai_et_al:LIPIcs.FSTTCS.2011.339, author = {Cai, Yang and Zhang, Ting}, title = {{A Tight Lower Bound for Streett Complementation}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {339--350}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.339}, URN = {urn:nbn:de:0030-drops-33474}, doi = {10.4230/LIPIcs.FSTTCS.2011.339}, annote = {Keywords: omega-automata, Streett automata, complementation, lower bounds} }

Document

**Published in:** LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logic, model-checking, program analysis and verification. For Streett complementation, a significant gap exists between the current lower bound 2^{Omega(n*log(n*k))} and upper bound 2^{O(n*k*log(n*k))}, where n is the state size, k is the number of Streett pairs, and k can be as large as 2^{n}. Determining the complexity of Streett complementation has been an open question since the late 80's. In this paper we show a complementation construction with upper bound 2^{O(n*log(n)+n*k*log(k))} for k=O(n) and 2^{O(n^{2}*log(n))} for k=Omega(n), which matches well the lower bound obtained in the paper arXiv:1102.2963. We also obtain a tight upper bound 2^{O(n*log(n))} for parity complementation.

Yang Cai and Ting Zhang. Tight Upper Bounds for Streett and Parity Complementation. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 112-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{cai_et_al:LIPIcs.CSL.2011.112, author = {Cai, Yang and Zhang, Ting}, title = {{Tight Upper Bounds for Streett and Parity Complementation}}, booktitle = {Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL}, pages = {112--128}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-32-3}, ISSN = {1868-8969}, year = {2011}, volume = {12}, editor = {Bezem, Marc}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.112}, URN = {urn:nbn:de:0030-drops-32269}, doi = {10.4230/LIPIcs.CSL.2011.112}, annote = {Keywords: Streett automata, omega-automata, parity automata, complementation, upper bounds} }

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