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Equilibrium Existence in Global Games With General Payoff Structures

Author

Listed:
  • Eric J. Hoffmann

    (West Texas A&M University)

  • Tarun Sabarwal

    (Department of Economics, The University of Kansas;)

Abstract
We consider global games with general payoff structures and prove existence of equilibrium. This shows that the global games method is well-defined with arbitrary strategic interaction among players, thus providing a foundation for the study of more general equilibrium behavior, especially as research in global games moves beyond the case of strategic complements. We also show that in every global game, even though the information of each player is correlated, the joint information measure is absolutely continuous with respect to the product of its marginals. As one application, the result here can be used to show existence of equilibrium in global games with both complementarity and congestion. This proves existence of equilibrium in a finite player version of the model in Karp, Lee, and Mason (2007), thus addressing a gap in the proof of equilibrium existence documented in Hoffmann and Sabarwal (2015).

Suggested Citation

  • Eric J. Hoffmann & Tarun Sabarwal, 2017. "Equilibrium Existence in Global Games With General Payoff Structures," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201702, University of Kansas, Department of Economics, revised Feb 2017.
    • Handle: RePEc:kan:wpaper:201702
    as

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    File URL: http://www2.ku.edu/~kuwpaper/2017Papers/201702.pdf
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    References listed on IDEAS

    as
    1. Oury, Marion, 2013. "Noise-independent selection in multidimensional global games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2638-2665.
    2. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    3. Hoffmann, Eric J. & Sabarwal, Tarun, 2015. "A global game with strategic substitutes and complements: Comment," Games and Economic Behavior, Elsevier, vol. 94(C), pages 188-190.
    4. 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.
    5. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    6. Karp, Larry & Lee, In Ho & Mason, Robin, 2007. "A global game with strategic substitutes and complements," Games and Economic Behavior, Elsevier, vol. 60(1), pages 155-175, July.
    7. Eric Hoffmann & Tarun Sabarwal, 2015. "A Global Game with Strategic Substitutes and Complements: Note," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201409, University of Kansas, Department of Economics.
    8. , & ,, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    9. Andrew J. Monaco & Tarun Sabarwal, 2016. "Games with strategic complements and substitutes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 65-91, June.
    10. 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.
    11. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2006. "Signaling in a Global Game: Coordination and Policy Traps," Journal of Political Economy, University of Chicago Press, vol. 114(3), pages 452-484, June.
    12. Basteck, Christian & Daniëls, Tijmen R. & Heinemann, Frank, 2013. "Characterising equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2620-2637.
    13. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    14. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2004. "The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information," Econometrica, Econometric Society, vol. 72(5), pages 1583-1599, September.
    15. Marion Oury, 2012. "Noise-Independent Selection in Multidimensional Global Games," THEMA Working Papers 2012-28, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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    Cited by:

    1. Rodrigo Harrison & Pedro Jara‐Moroni, 2021. "Global Games With Strategic Substitutes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(1), pages 141-173, February.
    2. Lee, Kyounghun & Oh, Frederick Dongchuhl, 2021. "Public information and global games with strategic complements and substitutes," Economics Letters, Elsevier, vol. 199(C).
    3. Lee, Kyounghun & Oh, Frederick Dongchuhl, 2021. "The role of large players in global games with strategic complements and substitutes," Economics Letters, Elsevier, vol. 198(C).

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    More about this item

    Keywords

    Global games; strategic complements; strategic substitutes; strategic heterogeneity; monotone games; equilibrium selection Women’s Health; Preventive Care; Ethnicity;
    All these keywords.

    JEL classification:

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

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