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LQG Information Design

Author

Listed:
  • Takashi Ui

    (Hitotsubashi University)

Abstract
A linear-quadratic-Gaussian (LQG) game is an incomplete information game with quadratic payoff functions and Gaussian information structures. It has many applications such as a Cournot game, a Bertrand game, a beauty contest game, and a network game among others. LQG information design is a problem to find an information structure from a given collection of feasible Gaussian information structures that maximizes a quadratic objective function when players follow a Bayes Nash equilibrium. This paper studies LQG information design by formulating it as semidefinite programming, which is a natural generalization of linear programming. Using the formulation, we provide sufficient conditions for optimality and suboptimality of no and full information disclosure. In the case of symmetric LQG games, we characterize the optimal symmetric information structure, and in the case of asymmetric LQG games, we characterize the optimal public information structure, each of which is in a closed-form expression.

Suggested Citation

  • Takashi Ui, 2020. "LQG Information Design," Working Papers on Central Bank Communication 018, University of Tokyo, Graduate School of Economics.
    • Handle: RePEc:upd:utmpwp:018
    as

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    File URL: https://www.centralbank.e.u-tokyo.ac.jp/wp-content/uploads/2020/03/cb-wp018.pdf
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    References listed on IDEAS

    as
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    12. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
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    17. Ricardo Alonso & Odilon Câmara, 2016. "Persuading Voters," American Economic Review, American Economic Association, vol. 106(11), pages 3590-3605, November.
    18. Nicky J. Welton & Howard H. Z. Thom, 2015. "Value of Information," Medical Decision Making, , vol. 35(5), pages 564-566, July.
    19. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    20. Laurent Mathevet & Jacopo Perego & Ina Taneva, 2020. "On Information Design in Games," Journal of Political Economy, University of Chicago Press, vol. 128(4), pages 1370-1404.
    21. Stephen Morris & Hyun Song Shin, 2002. "Social Value of Public Information," American Economic Review, American Economic Association, vol. 92(5), pages 1521-1534, December.
    22. Ui, Takashi & Yoshizawa, Yasunori, 2015. "Characterizing social value of information," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 507-535.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Furkan Sezer & Ceyhun Eksin, 2022. "Information Preferences of Individual Agents in Linear-Quadratic-Gaussian Network Games," Papers 2203.13056, arXiv.org.
    2. Furkan Sezer & Hossein Khazaei & Ceyhun Eksin, 2021. "Maximizing Social Welfare and Agreement via Information Design in Linear-Quadratic-Gaussian Games," Papers 2102.13047, arXiv.org, revised Feb 2023.
    3. Takashi Ui, 2022. "Impacts of Public Information on Flexible Information Acquisition," Papers 2204.09250, arXiv.org, revised Apr 2022.
    4. Takashi Ui, 2022. "Optimal and Robust Disclosure of Public Information," Papers 2203.16809, arXiv.org, revised Apr 2022.
    5. Takashi Ui, 2022. "Optimal and Robust Disclosure of Public Information," Working Papers on Central Bank Communication 039, University of Tokyo, Graduate School of Economics.

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    More about this item

    Keywords

    incomplete information games; optimal information structures; information design; Bayesian persuasion;
    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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