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Characterizing social value of information

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  • Ui, Takashi
  • Yoshizawa, Yasunori

Abstract

This paper characterizes the social value of information in Bayesian games with symmetric quadratic payoff functions and normally distributed public and private signals. The main result provides a necessary and sufficient condition for welfare to increase with public or private information. In so doing, we represent welfare as a linear combination of the variance of a common term in an equilibrium strategy and that of an idiosyncratic term, which are referred to as the common variance and the idiosyncratic variance of actions, respectively. The ratio of their coefficients is a key parameter in our condition. If the coefficient of the common variance is relatively large, welfare necessarily increases, but if it is relatively small, welfare can decrease. Using our condition, we find eight types of games with different welfare effects of information.

Suggested Citation

  • Ui, Takashi & Yoshizawa, Yasunori, 2015. "Characterizing social value of information," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 507-535.
    • Handle: RePEc:eee:jetheo:v:158:y:2015:i:pb:p:507-535
    DOI: 10.1016/j.jet.2014.12.007
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    3. Franzkeit, Janna & Schwientek, Anne Kathrina & Jahn, Carlos, 2020. "Stowage planning for inland container vessels: A literature review," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Jahn, Carlos & Kersten, Wolfgang & Ringle, Christian M. (ed.), Data Science in Maritime and City Logistics: Data-driven Solutions for Logistics and Sustainability. Proceedings of the Hamburg International Conferen, volume 30, pages 247-280, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    4. Camille Cornand & Rodolphe Dos Santos Ferreira, 2020. "The social value of information and the competition motive: price versus quantity games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1101-1137, November.
    5. Yanwei Jia & Jussi Keppo & Ville Satopää, 2023. "Herding in Probabilistic Forecasts," Management Science, INFORMS, vol. 69(5), pages 2713-2732, May.
    6. Takashi Ui, 2022. "Impacts of Public Information on Flexible Information Acquisition," Papers 2204.09250, arXiv.org, revised Apr 2022.
    7. Arato, Hiroki & Hori, Takeo & Nakamura, Tomoya, 2021. "Endogenous information acquisition and the partial announcement policy," Information Economics and Policy, Elsevier, vol. 55(C).
    8. Takashi Ui, 2022. "Optimal and Robust Disclosure of Public Information," Papers 2203.16809, arXiv.org, revised Apr 2022.
    9. Cumbul, Eray, 2021. "Stackelberg versus Cournot oligopoly with private information," International Journal of Industrial Organization, Elsevier, vol. 74(C).
    10. Ui, Takashi & 宇井, 貴志, 2019. "The Lucas Imperfect Information Model with Imperfect Common Knowledge," Discussion Papers 2019-04, Graduate School of Economics, Hitotsubashi University.
    11. UI, Takashi & 宇井, 貴志, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    12. Yuki Amemiya & Akifumi Ishihara & Tomoya Nakamura, 2021. "Pre‐emptive production and market competitiveness in oligopoly with private information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(2), pages 449-455, May.
    13. Camille Cornand & Rodolphe dos Santos Ferreira, 2017. "The social value of information and the competition motive: Price vs. quantity games," Working Papers halshs-01614815, HAL.
    14. Masaki Miyashita & Takashi Ui, 2023. "LQG Information Design," Papers 2312.09479, arXiv.org, revised Jun 2024.
    15. Leister, C. Matthew, 2020. "Information acquisition and welfare in network games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 453-475.
    16. Szkup, Michal, 2020. "Multiplier effect and comparative statics in global games of regime change," Theoretical Economics, Econometric Society, vol. 15(2), May.
    17. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    18. Takashi Ui, 2022. "Optimal and Robust Disclosure of Public Information," Working Papers on Central Bank Communication 039, University of Tokyo, Graduate School of Economics.
    19. Pavan, Alessandro & Vives, Xavier, 2015. "Information, Coordination, and Market Frictions: An Introduction," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 407-426.
    20. Takashi Ui, 2019. "The Lucas Imperfect Information Model with Imperfect Common Knowledge," Working Papers on Central Bank Communication 007, University of Tokyo, Graduate School of Economics.
    21. Lee, Kyounghun & Oh, Frederick Dongchuhl, 2021. "Public information and global games with strategic complements and substitutes," Economics Letters, Elsevier, vol. 199(C).
    22. Takashi Ui, 2020. "The Lucas imperfect information model with imperfect common knowledge," The Japanese Economic Review, Springer, vol. 71(1), pages 85-100, January.
    23. Anna Bayona, 2018. "The social value of information with an endogenous public signal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 1059-1087, December.
    24. Takashi Ui, 2020. "LQG Information Design," Working Papers on Central Bank Communication 018, University of Tokyo, Graduate School of Economics.
    25. Masaki Miyashita & Takashi Ui, 2024. "On the Pettis Integral Approach to Large Population Games," Papers 2403.17605, arXiv.org.

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    More about this item

    Keywords

    Bayesian game; Incomplete information; Optimal information structure; Potential game; Private signal; Public signal; Team; Value of information;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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