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Monotone Comparative Statics for Games with Strategic Substitutes

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  • Roy, Sunanda
  • Sabarwal, Tarun

Abstract

This paper studies comparative statics of equilibria in models where the optimal responses under consideration are (weakly) decreasing in endogenous variables, and (weakly) increasing in exogenous parameters. Such models include parameterized games of strategic substitutes. The analysis provides a sufficient condition for existence of increasing equilibria at a higher parameter value. This condition is presented first for best-response functions; it can be translated easily to payoff functions with one-dimensional individual strategy spaces, and it has a natural analogue to best-response correspondences. The condition is tight in the sense that with a weakenened condition, the same result may not obtain. The results here apply to asymmetric equilibria, and are applied to two classes of examples -- Cournot duopoly and tournaments. Moreover, sufficient conditions are presented to exhibit strong comparative statics of equilibria (that is, every equilibrium at a higher parameter value is greater than a given equilibrium at a lower parameter value), and to show existence of increasing equilibrium selections.

Suggested Citation

  • Roy, Sunanda & Sabarwal, Tarun, 2005. "Monotone Comparative Statics for Games with Strategic Substitutes," MPRA Paper 4709, University Library of Munich, Germany, revised 04 Sep 2007.
  • Handle: RePEc:pra:mprapa:4709
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    References listed on IDEAS

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    Cited by:

    1. Shirai, Koji, 2010. "An existence theorem for Cournot-Walras equilibria in a monopolistically competitive economy," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1093-1102, November.
    2. Eric Hoffmann, 2013. "Global Games Selection in Games with Strategic Substitutes or Complements," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201308, University of Kansas, Department of Economics.
    3. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    4. 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.
    5. Alexandrov, Alexei & Bedre-Defolie, Özlem, 2017. "LeChatelier–Samuelson principle in games and pass-through of shocks," Journal of Economic Theory, Elsevier, vol. 168(C), pages 44-54.
    6. Feng, Yue & Sabarwal, Tarun, 2020. "Strategic complements in two stage, 2 × 2 games," Journal of Economic Theory, Elsevier, vol. 190(C).
    7. Bertrand Koebel & François Laisney, 2014. "Aggregation with Cournot Competition: the Le Chatelier Samuelson Principle," Annals of Economics and Statistics, GENES, issue 115-116, pages 343-360.
    8. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    9. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    10. Peter Arendorf Bache & Anders Laugesen, 2013. "Monotone Comparative Statics for the Industry Composition," Economics Working Papers 2013-10, Department of Economics and Business Economics, Aarhus University.
    11. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    12. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    13. Anne-Christine Barthel & Eric Hoffmann, 2020. "Characterizing monotone games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1045-1068, November.
    14. Alexei Alexandrov & Özlem Bedre-Defolie, 2015. "LeChatelier-Samuelson principle in games and pass-through of shocks," ESMT Research Working Papers ESMT-15-03, ESMT European School of Management and Technology, revised 01 Mar 2016.
    15. Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
    16. Hoffmann, Eric, 2016. "On the learning and stability of mixed strategy Nash equilibria in games of strategic substitutes," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 349-362.
    17. Eddie Dekel & Ady Pauzner, 2018. "Uniqueness, stability and comparative statics for two-person Bayesian games with strategic substitutes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 747-761, October.
    18. Anne-Christine Barthel & Eric Hoffmann, 2019. "Rationalizability and learning in games with strategic heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 565-587, April.
    19. Bilanakosa, Christos & Heywood, John S. & Sessions, John & Theodoropoulos, Nikolaos, 2017. "Worker Training and Quality Competition," GLO Discussion Paper Series 137, Global Labor Organization (GLO).
    20. Minji Bang & Wayne Yuan Gao & Andrew Postlewaite & Holger Sieg, 2021. "Estimating Production Functions with Partially Latent Inputs," Papers 2101.05847, arXiv.org, revised Apr 2021.
    21. Yue Feng & Tarun Sabarwal, 2020. "Dynamic strategic complements in two stage, 2x2 games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202006, University of Kansas, Department of Economics.
    22. Martin Kaae Jensen, 2015. "Existence, Uniqueness, and Comparative Statics in Contests," Discussion Papers in Economics 15/16, Division of Economics, School of Business, University of Leicester.

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    More about this item

    Keywords

    Monotone comparative statics; Weakly decreasing functions; Strategic substitutes; Payoff functions;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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