IDEAS home Printed from https://ideas.repec.org/p/mpg/wpaper/2019_14.html
   My bibliography  Save this paper

Incomplete-Information Games in Large Populations with Anonymity

Author

Listed:
  • Martin Hellwig

    (Max Planck Institute for Research on Collective Goods)

Abstract

The paper provides mathematical foundations for modeling strategic interdependence with a continuum of agents where uncertainty has an aggregate component and an agent-speci?c component and the latter satis?es a conditional law of large numbers. This decomposition of uncertainty is implied by a condition of anonymity in beliefs, under which the agent in question considers the other agents? types to be essentially pairwise exchangeable. If there is also anonymity in payoff functions, all strategically relevant aspects of beliefs are contained in an agent?s macro beliefs about the cross-section distribution of the other agents?types. The paper also gives conditions under which a function assigning macro beliefs to types is compatible with the existence of a common prior. Key Words: Incomplete-information games, large populations, belief functions, common priors, exchangeability, conditional independence, conditional exact law of large numbers.

Suggested Citation

  • Martin Hellwig, 2019. "Incomplete-Information Games in Large Populations with Anonymity," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2019_14, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2019_14
    as

    Download full text from publisher

    File URL: http://www.coll.mpg.de/pdf_dat/2019_14online.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jean-Charles Rochet & Xavier Vives, 2004. "Coordination Failures and the Lender of Last Resort: Was Bagehot Right After All?," Journal of the European Economic Association, MIT Press, vol. 2(6), pages 1116-1147, December.
    2. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    3. Assar Lindbeck & Jörgen Weibull, 1987. "Balanced-budget redistribution as the outcome of political competition," Public Choice, Springer, vol. 52(3), pages 273-297, January.
    4. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    5. Postlewaite, Andrew & Vives, Xavier, 1987. "Bank Runs as an Equilibrium Phenomenon," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 485-491, June.
    6. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    7. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    8. Felix J. Bierbrauer, 2014. "Optimal Tax and Expenditure Policy with Aggregate Uncertainty," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 205-257, February.
    9. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    10. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    11. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    12. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    13. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    14. Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 743-766, March.
    15. Iván Werning & George-Marios Angeletos, 2006. "Crises and Prices: Information Aggregation, Multiplicity, and Volatility," American Economic Review, American Economic Association, vol. 96(5), pages 1720-1736, December.
    16. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    17. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
    18. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
    19. Marianne Bertrand & Sendhil Mullainathan, 2004. "Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination," American Economic Review, American Economic Association, vol. 94(4), pages 991-1013, September.
    20. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    21. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    22. Alberto Alesina & Guido Tabellini, 1990. "A Positive Theory of Fiscal Deficits and Government Debt," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 403-414.
    23. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    24. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    25. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. Itay Goldstein & Ady Pauzner, 2005. "Demand–Deposit Contracts and the Probability of Bank Runs," Journal of Finance, American Finance Association, vol. 60(3), pages 1293-1327, June.
    27. Lei Qiao & Yeneng Sun & Zhixiang Zhang, 2016. "Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 43-64, June.
    28. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    29. Albert S. Kyle, 1989. "Informed Speculation with Imperfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 317-355.
    30. Hellwig, Christian, 2002. "Public Information, Private Information, and the Multiplicity of Equilibria in Coordination Games," Journal of Economic Theory, Elsevier, vol. 107(2), pages 191-222, December.
    31. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    32. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    33. Bryant, John, 1980. "A model of reserves, bank runs, and deposit insurance," Journal of Banking & Finance, Elsevier, vol. 4(4), pages 335-344, December.
    34. Sanford J. Grossman & Oliver D. Hart, 1980. "Takeover Bids, the Free-Rider Problem, and the Theory of the Corporation," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 42-64, Spring.
    35. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
    36. Bierbrauer, Felix, 2009. "A note on optimal income taxation, public goods provision and robust mechanism design," Journal of Public Economics, Elsevier, vol. 93(5-6), pages 667-670, June.
    37. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).
    2. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.

    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. Xavier Vives, 2014. "Strategic Complementarity, Fragility, and Regulation," The Review of Financial Studies, Society for Financial Studies, vol. 27(12), pages 3547-3592.
    2. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
    3. Dunhong Jin & Marcin Kacperczyk & Bige Kahraman & Felix Suntheim, 2022. "Swing Pricing and Fragility in Open-End Mutual Funds," The Review of Financial Studies, Society for Financial Studies, vol. 35(1), pages 1-50.
    4. Assaf Razin & Itay Goldstein, 2012. "Review Of Theories of Financial Crises," 2012 Meeting Papers 214, Society for Economic Dynamics.
    5. Fiorini, Luciana C. & Rodrigues-Neto, José A., 2017. "Self-consistency, consistency and cycles in non-partitional knowledge models," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 11-21.
    6. Alexander Zimper, 2013. "Optimal Liquidity Provision Through a Demand Deposit Scheme: The Jacklin Critique Revisited," German Economic Review, Verein für Socialpolitik, vol. 14(1), pages 89-107, February.
    7. 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.
    8. Zhang, Jinqing & He, Liang & An, Yunbi, 2020. "Measuring banks’ liquidity risk: An option-pricing approach," Journal of Banking & Finance, Elsevier, vol. 111(C).
    9. Zhiguo He & Wei Xiong, 2012. "Dynamic Debt Runs," The Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1799-1843.
    10. Xavier Vives, 2011. "Competition and Stability in Banking," Central Banking, Analysis, and Economic Policies Book Series, in: Luis Felipe Céspedes & Roberto Chang & Diego Saravia (ed.),Monetary Policy under Financial Turbulence, edition 1, volume 16, chapter 12, pages 455-502, Central Bank of Chile.
    11. Anat R. Admati & Peter M. DeMarzo & Martin F. Hellwig & Paul Pfleiderer, 2010. "Fallacies, Irrelevant Facts, and Myths in the Discussion of Capital Regulation: Why Bank Equity is Not Expensive," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2010_42, Max Planck Institute for Research on Collective Goods.
    12. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    13. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.
    14. Toni Ahnert & Ali Kakhbod, 2017. "Information Choice and Amplification of Financial Crises," The Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 2130-2178.
    15. José Alvaro Rodrigues-Neto, 2012. "Cycles of length two in monotonic models," ANU Working Papers in Economics and Econometrics 2012-587, Australian National University, College of Business and Economics, School of Economics.
    16. Edmond, Chris, 2018. "Non-Laplacian beliefs in a global game with noisy signaling," Research in Economics, Elsevier, vol. 72(2), pages 297-312.
    17. Luciana C. Fiorini & José A. Rodrigues-Neto, 2014. "Self-Consistency and Common Prior in Non-Partitional Knowledge Models," ANU Working Papers in Economics and Econometrics 2014-621, Australian National University, College of Business and Economics, School of Economics.
    18. Lawrence Schmidt & Allan Timmermann & Russ Wermers, 2016. "Runs on Money Market Mutual Funds," American Economic Review, American Economic Association, vol. 106(9), pages 2625-2657, September.
    19. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    20. Yi, Ming, 2017. "Speculator-triggered crisis and interventions," Journal of Macroeconomics, Elsevier, vol. 52(C), pages 135-146.

    More about this item

    Keywords

    Monetary union; central banking; politics of banks; banking union; bank resolution; bail-in.;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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

    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:mpg:wpaper:2019_14. 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: Marc Martin (email available below). General contact details of provider: https://edirc.repec.org/data/mppggde.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.