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Bayesian comparative statics

Author

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  • Mekonnen, Teddy

    (Department of Economics, Brown University)

  • Leal Vizcaíno, René

    (Economics Research Division, Banco de México)

Abstract

We study how changes to the informativeness of signals in Bayesian games and single-agent decision problems affect the distribution of equilibrium actions. Focusing on supermodular environments, we provide conditions under which a more precise private signal for one agent leads to an increasing-mean spread or a decreasing-mean spread of equilibrium actions for all agents. We apply our comparative statics to information disclosure games between a sender and many receivers and derive sufficient conditions on the primitive payoffs that lead to extremal disclosure of information.

Suggested Citation

  • Mekonnen, Teddy & Leal Vizcaíno, René, 2022. "Bayesian comparative statics," Theoretical Economics, Econometric Society, vol. 17(1), January.
  • Handle: RePEc:the:publsh:4345
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    References listed on IDEAS

    as
    1. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
    2. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    3. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    4. Richard N. Clarke, 1983. "Collusion and the Incentives for Information Sharing," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 383-394, Autumn.
    5. Gal-Or, Esther, 1985. "Information Sharing in Oligopoly," Econometrica, Econometric Society, vol. 53(2), pages 329-343, March.
    6. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    7. Luis Rayo & Ilya Segal, 2010. "Optimal Information Disclosure," Journal of Political Economy, University of Chicago Press, vol. 118(5), pages 949-987.
    8. Fudenberg, Drew & Tirole, Jean, 1984. "The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look," American Economic Review, American Economic Association, vol. 74(2), pages 361-366, May.
    9. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    10. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-574, September.
    11. George-Marios Angeletos & Alessandro Pavan, 2007. "Efficient Use of Information and Social Value of Information," Econometrica, Econometric Society, vol. 75(4), pages 1103-1142, July.
    12. George-Marios Angeletos & Alessandro Pavan, 2009. "Policy with Dispersed Information," Journal of the European Economic Association, MIT Press, vol. 7(1), pages 11-60, March.
    13. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
    14. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    15. Luca Colombo & Gianluca Femminis & Alessandro Pavan, 2014. "Information Acquisition and Welfare," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1438-1483.
    16. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    17. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    18. Piotr Dworczak & Giorgio Martini, 2019. "The Simple Economics of Optimal Persuasion," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 1993-2048.
    19. Martin Kaae Jensen, 2018. "Distributional Comparative Statics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 581-610.
    20. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    21. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    22. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    23. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, April.
    24. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    25. Amir, Rabah & Lazzati, Natalia, 2016. "Endogenous information acquisition in Bayesian games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 163(C), pages 684-698.
    26. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    27. Christian Hellwig & Laura Veldkamp, 2009. "Knowing What Others Know: Coordination Motives in Information Acquisition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 223-251.
    28. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    29. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
    30. Guido Lorenzoni, 2010. "Optimal Monetary Policy with Uncertain Fundamentals and Dispersed Information ," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 305-338.
    31. Ozan Candogan & Kostas Bimpikis & Asuman Ozdaglar, 2012. "Optimal Pricing in Networks with Externalities," Operations Research, INFORMS, vol. 60(4), pages 883-905, August.
    32. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    33. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    34. 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.
    35. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    36. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    37. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414, Elsevier.
    38. Stephen Morris & Hyun Song Shin, 2002. "Social Value of Public Information," American Economic Review, American Economic Association, vol. 92(5), pages 1521-1534, December.
    39. William Novshek & Hugo Sonnenschein, 1982. "Fulfilled Expectations Cournot Duopoly with Information Acquisition and Release," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 214-218, Spring.
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    1. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.
    2. Andres Espitia, 2024. "Confidence and Organizations," CRC TR 224 Discussion Paper Series crctr224_2024_521, University of Bonn and University of Mannheim, Germany.

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    More about this item

    Keywords

    Comparative statics; supermodular order; convex order; information disclosure;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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