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Optimal Transport of Information

Author

Listed:
  • Semyon Malamud

    (Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute)

  • Anna Cieslak

    (Duke University - Fuqua School of Business; National Bureau of Economic Research (NBER))

  • Andreas Schrimpf

    (Bank for International Settlements (BIS) - Monetary and Economic Department)

Abstract

We study the general problem of optimal information design with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of an infinite signal space and characterize the solution in terms of a Monge-Kantorovich optimal transport problem with an endogenous information transport cost. We use our novel approach to: 1. Derive necessary and sufficient conditions for optimality based on Bregman divergences for non-convex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a non-linear, second-order partial differential equation whose solutions correspond to regular optimal policies.

Suggested Citation

  • Semyon Malamud & Anna Cieslak & Andreas Schrimpf, 2021. "Optimal Transport of Information," Swiss Finance Institute Research Paper Series 21-15, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2115
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    References listed on IDEAS

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    1. Calzolari, Giacomo & Pavan, Alessandro, 2006. "On the optimality of privacy in sequential contracting," Journal of Economic Theory, Elsevier, vol. 130(1), pages 168-204, September.
    2. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    3. Dirk Bergemann & Stephen Morris, 2016. "Information Design, Bayesian Persuasion, and Bayes Correlated Equilibrium," American Economic Review, American Economic Association, vol. 106(5), pages 586-591, May.
    4. Dmitry Kramkov & Yan Xu, 2019. "An optimal transport problem with backward martingale constraints motivated by insider trading," Papers 1906.03309, arXiv.org.
    5. Wei, K C John & Lee, Cheng F & Lee, Alice C, 1999. "Linear Conditional Expectation, Return Distributions, and Capital Asset Pricing Theories," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(4), pages 471-487, Winter.
    6. J. Hugonnier & S. Malamud & E. Trubowitz, 2012. "Endogenous Completeness of Diffusion Driven Equilibrium Markets," Econometrica, Econometric Society, vol. 80(3), pages 1249-1270, May.
    7. Michael Ostrovsky & Michael Schwarz, 2010. "Information Disclosure and Unraveling in Matching Markets," American Economic Journal: Microeconomics, American Economic Association, vol. 2(2), pages 34-63, May.
    8. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    9. Hugo Hopenhayn & Maryam Saeedi, 2019. "Optimal Ratings and Market Outcomes," NBER Working Papers 26221, National Bureau of Economic Research, Inc.
    10. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    11. Jon Kleinberg & Sendhil Mullainathan, 2019. "Simplicity Creates Inequity: Implications for Fairness, Stereotypes, and Interpretability," NBER Working Papers 25854, National Bureau of Economic Research, Inc.
    12. Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
    13. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    14. Smith, Cyril & Knott, Martin, 1992. "On Hoeffding-Fréchet bounds and cyclic monotone relations," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 328-334, February.
    15. K. C. John Wei & Cheng F. Lee & Alice C. Lee, 1999. "Linear Conditional Expectation, Return Distributions, And Capital Asset Pricing Theories," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(4), pages 471-487, December.
    16. Pavan, Alessandro & Dworczak, Piotr, 2020. "Preparing for the Worst But Hoping for the Best: Robust (Bayesian) Persuasion," CEPR Discussion Papers 15017, C.E.P.R. Discussion Papers.
    17. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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    Cited by:

    1. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Persuasion as Transportation," Papers 2307.07672, arXiv.org.

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    More about this item

    Keywords

    Bayesian Persuasion; Information Design; Signalling; Optimal Transport;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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