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Common belief foundations of global games

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  • Morris, Stephen
  • Shin, Hyun Song
  • Yildiz, Muhamet

Abstract

We study coordination games under general type spaces. We characterize rationalizable actions in terms of the properties of the belief hierarchies and show that there is a unique rationalizable action played whenever there is approximate common certainty of rank beliefs, defined as the probability the players assign to their payoff parameters being higher than their opponents'. We argue that this is the driving force behind selection results for the specific type spaces in the global games literature.

Suggested Citation

  • Morris, Stephen & Shin, Hyun Song & Yildiz, Muhamet, 2016. "Common belief foundations of global games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 826-848.
  • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:826-848
    DOI: 10.1016/j.jet.2016.03.007
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    1. Van Zandt, Timothy, 2010. "Interim Bayesian Nash equilibrium on universal type spaces for supermodular games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 249-263, January.
    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. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
    4. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    5. Laurent Mathevet, 2010. "A contraction principle for finite global games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 539-563, March.
    6. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, January.
    7. Stephen Morris & Hyun Song Shin, 2012. "Contagious Adverse Selection," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 1-21, January.
    8. Morris, Stephen & Shin, Hyun Song, 2004. "Coordination risk and the price of debt," European Economic Review, Elsevier, vol. 48(1), pages 133-153, February.
    9. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    10. 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.
    11. Guillaume Plantin & Haresh Sapra & Hyun Song Shin, 2008. "Marking-to-Market: Panacea or Pandora's Box?," Journal of Accounting Research, Wiley Blackwell, vol. 46(2), pages 435-460, May.
    12. Mason, Robin & Valentinyi, Ã kos, 2007. "The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games," Discussion Paper Series In Economics And Econometrics 0710, Economics Division, School of Social Sciences, University of Southampton.
    13. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    14. Rossella Argenziano, 2008. "Differentiated networks: equilibrium and efficiency," RAND Journal of Economics, RAND Corporation, vol. 39(3), pages 747-769.
    15. Michael Woodford, 2005. "Central bank communication and policy effectiveness," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, issue Aug, pages 399-474.
    16. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2003. "Coordination and Policy Traps," NBER Working Papers 9767, National Bureau of Economic Research, Inc.
    17. Stephen Morris & Hyun Song Shin, 2001. "Rethinking Multiple Equilibria in Macroeconomic Modeling," NBER Chapters,in: NBER Macroeconomics Annual 2000, Volume 15, pages 139-182 National Bureau of Economic Research, Inc.
    18. 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.
    19. Aleh Tsyvinski & Arijit Mukherji & Christian Hellwig, 2006. "Self-Fulfilling Currency Crises: The Role of Interest Rates," American Economic Review, American Economic Association, vol. 96(5), pages 1769-1787, December.
    20. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    21. Sergei Izmalkov & Muhamet Yildiz, 2010. "Investor Sentiments," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 21-38, February.
    22. 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.
    23. Morris, Stephen & Shin, Hyun Song & Yildiz, Muhamet, 2016. "Common belief foundations of global games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 826-848.
    24. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    25. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    26. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    27. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Cited by:

    1. Mostafa Beshkar & Jee-Hyeong Park, 2017. "Dispute Settlement with Second-Order Uncertainty: The Case of International Trade Disputes," Caepr Working Papers 2017-010 Classification-K, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    2. Morris, Stephen & Shin, Hyun Song & Yildiz, Muhamet, 2016. "Common belief foundations of global games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 826-848.
    3. Canale, M. & Fagiano, L. & Milanese, M., 2009. "KiteGen: A revolution in wind energy generation," Energy, Elsevier, vol. 34(3), pages 355-361.
    4. Morris, Stephen & Shim, Ilhyock & Shin, Hyun Song, 2017. "Redemption risk and cash hoarding by asset managers," Journal of Monetary Economics, Elsevier, vol. 89(C), pages 71-87.
    5. Dominik Grafenhofer & Wolfgang Kuhle, 2015. "Observing Each Other's Observations in a Bayesian Coordination Game," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_18, Max Planck Institute for Research on Collective Goods.
    6. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    7. Mathevet, Laurent, 2014. "Beliefs and rationalizability in games with complementarities," Games and Economic Behavior, Elsevier, vol. 85(C), pages 252-271.
    8. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2007. "Efficient dynamic coordination with individual learning," LSE Research Online Documents on Economics 24498, London School of Economics and Political Science, LSE Library.
    9. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    10. World Bank & Nicholas Institute, 2016. "Tuna Fisheries," World Bank Other Operational Studies 28412, The World Bank.
    11. Stephen Morris & Ming Yang, 2016. "Coordination and Continuous Choice," Working Papers 087_2017, Princeton University, Department of Economics, Econometric Research Program..
    12. repec:eee:macchp:v2-1065 is not listed on IDEAS
    13. repec:wly:iecrev:v:57:y:2016:i::p:1135-1148 is not listed on IDEAS
    14. Laurent Mathevet, 2010. "A contraction principle for finite global games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 539-563, March.
    15. Stephen Morris & Ming Yang, 2016. "Coordination and the Relative Cost of Distinguishing Nearby States," Working Papers 079_2016, Princeton University, Department of Economics, Econometric Research Program..
    16. Dominik Grafenhofer & Wolgang Kuhle, 2014. "Observing Each Other's Observations in the Electronic Mail Game," Papers 1501.00882, arXiv.org.
    17. Chen, Yi-Chun, 2012. "A structure theorem for rationalizability in the normal form of dynamic games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 587-597.
    18. Grafenhofer, Dominik & Kuhle, Wolfgang, 2016. "Observing each other’s observations in a Bayesian coordination game," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 10-17.
    19. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2012. "Dynamic coordination with individual learning," Games and Economic Behavior, Elsevier, vol. 74(1), pages 83-101.
    20. Sergei Izmalkov & Muhamet Yildiz, 2010. "Investor Sentiments," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 21-38, February.
    21. Stephen Morris & Hyun Song Shin, 2016. "Illiquidity Component Of Credit Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 1135-1148, November.

    More about this item

    Keywords

    Global games; Risk-dominance; Rank beliefs; Higher-order beliefs; Rationalizability;

    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
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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