Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1821.html
   My bibliography  Save this paper

Robust Predictions in Games with Incomplete Information

Author

Listed:
Abstract
We analyze games of incomplete information and offer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set of Bayes Nash equilibria and the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior information of the analyst refines the set of equilibrium distribution. As an application, we obtain new results regarding the optimal information sharing policy of firms under demand uncertainty. Finally, we reverse the perspective and investigate the identification problem under concerns for robustness to private information. We show how the presence of private information leads to partial rather than complete identification of the structural parameters of the game. As a prominent example we analyze the canonical problem of demand and supply identification.

Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2011. "Robust Predictions in Games with Incomplete Information," Cowles Foundation Discussion Papers 1821, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1821
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d18/d1821.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    2. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    3. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    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. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2013. "Extremal Information Structures in the First Price Auction," Working Papers 055-2013, Princeton University, Department of Economics, Econometric Research Program..
    6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    7. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
    8. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    9. Luis Rayo & Ilya Segal, 2010. "Optimal Information Disclosure," Journal of Political Economy, University of Chicago Press, vol. 118(5), pages 949-987.
    10. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    11. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, January.
    12. de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    13. 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.
    14. 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.
    15. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    16. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    17. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(2), pages 223-227.
    18. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    19. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    20. Bergemann, Dirk & Pesendorfer, Martin, 2007. "Information structures in optimal auctions," Journal of Economic Theory, Elsevier, vol. 137(1), pages 580-609, November.
    21. Andrew Sweeting, 2009. "The strategic timing incentives of commercial radio stations: An empirical analysis using multiple equilibria," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 710-742, December.
    22. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    23. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    24. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
    25. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 215-218, December.
    26. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
    27. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," LIDAM Discussion Papers CORE 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    28. Alison J. Kirby, 1988. "Trade Associations as Information Exchange Mechanisms," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 138-146, Spring.
    29. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    30. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:cwl:cwldpp:1821rr is not listed on IDEAS
    2. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    3. repec:pri:metric:wp023_2011_bergemann_morris.pdf is not listed on IDEAS
    4. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    5. Mekonnen, Teddy & Leal Vizcaíno, René, 2022. "Bayesian comparative statics," Theoretical Economics, Econometric Society, vol. 17(1), January.
    6. Bergemann, Dirk & Heumann, Tibor & Morris, Stephen, 2015. "Information and volatility," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 427-465.
    7. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    8. Myatt, David P. & Wallace, Chris, 2015. "Cournot competition and the social value of information," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 466-506.
    9. Carroll, Gabriel, 2016. "Informationally robust trade and limits to contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 334-361.
    10. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    11. Angeletos, G.-M. & Lian, C., 2016. "Incomplete Information in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1065-1240, Elsevier.
    12. Myeonghwan Cho, 2019. "Investor’s Information Sharing with Firms in Oligopoly," Korean Economic Review, Korean Economic Association, vol. 35, pages 439-469.
    13. Alessandro Bonatti & Dirk Bergemann, 2012. "Markets for Data," 2012 Meeting Papers 538, Society for Economic Dynamics.
    14. Roy, Jaideep & Silvers, Randy & Sun, Ching-Jen, 2019. "Majoritarian preference, utilitarian welfare and public information in Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 116(C), pages 269-288.
    15. Sjaak Hurkens, 2014. "Bayesian Nash equilibrium in “linear” Cournot models with private information about costs," International Journal of Economic Theory, The International Society for Economic Theory, vol. 10(2), pages 203-217, June.
    16. Hyoduk Shin & Tunay I. Tunca, 2010. "Do Firms Invest in Forecasting Efficiently? The Effect of Competition on Demand Forecast Investments and Supply Chain Coordination," Operations Research, INFORMS, vol. 58(6), pages 1592-1610, December.
    17. Goltsman, Maria & Pavlov, Gregory, 2014. "Communication in Cournot oligopoly," Journal of Economic Theory, Elsevier, vol. 153(C), pages 152-176.
    18. Qiu, Larry D. & Zhou, Wen, 2006. "International mergers: Incentives and welfare," Journal of International Economics, Elsevier, vol. 68(1), pages 38-58, January.
    19. António Brandão & Joana Pinho, 2015. "Asymmetric Information And Exchange Of Information About Product Differentiation," Bulletin of Economic Research, Wiley Blackwell, vol. 67(2), pages 166-185, April.
    20. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    21. Medín, J. Andrés Faíña & Rodríguez, Jesús López & Rodríguez, José López, 2003. "Information Exchanges in Cournot Duopolies," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 57(1), January.
    22. Pavan, Alessandro & Vives, Xavier, 2015. "Information, Coordination, and Market Frictions: An Introduction," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 407-426.
    23. Takashi Ui & Stephen Morris, 2020. "Incomplete Information Robustness," Working Papers on Central Bank Communication 019, University of Tokyo, Graduate School of Economics.

    More about this item

    Keywords

    Incomplete information; Correlated equilibrium; Robustness to private information; Moments restrictions; Identification; Information bounds;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1821. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.