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Monotone Comparative Statics for Games With Strategic Substitutes

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  • Sunanda Roy

    (College of Business and Public Administration, Drake University)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

Abstract

Under some conditions, parameterized games with strategic substitutes exhibit monotone comparative statics of equilibria. These conditions relate to a tradeoff between a direct parameter effect and an opposing, indirect strategic substitute effect. If the indirect effect does not dominate the direct effect, monotone comparative statics of equilibria are guaranteed. These conditions are available for best-response functions, differentiable payoff functions, and general payoff functions. Results are extended to correspondences, the analysis applies to asymmetric equilibria, and several examples are provided.

Suggested Citation

  • Sunanda Roy & Tarun Sabarwal, 2008. "Monotone Comparative Statics for Games With Strategic Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200810, University of Kansas, Department of Economics, revised May 2010.
    • Handle: RePEc:kan:wpaper:200810
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    8. 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.
    9. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    10. 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.
    11. 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.
    12. Feng, Yue & Sabarwal, Tarun, 2020. "Strategic complements in two stage, 2 × 2 games," Journal of Economic Theory, Elsevier, vol. 190(C).
    13. Tigran Melkonyan & Surajeet Chakravarty, 2024. "Pre‐play promises, threats and commitments under partial credibility," Economic Inquiry, Western Economic Association International, vol. 62(1), pages 308-328, January.
    14. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    15. 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.
    16. 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.
    17. Lukasz Balbus & Wojciech Olszewski & Kevin Reffett & Lukasz Wozny, 2022. "Iterative Monotone Comparative Statics," KAE Working Papers 2022-072, Warsaw School of Economics, Collegium of Economic Analysis.
    18. 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.
    19. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    20. Bilanakosa, Christos & Heywood, John S. & Sessions, John & Theodoropoulos, Nikolaos, 2017. "Worker Training and Quality Competition," GLO Discussion Paper Series 137, Global Labor Organization (GLO).
    21. Bang, Minji & Gao, Wayne Yuan & Postlewaite, Andrew & Sieg, Holger, 2023. "Using monotonicity restrictions to identify models with partially latent covariates," Journal of Econometrics, Elsevier, vol. 235(2), pages 892-921.
    22. 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.
    23. 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.
    24. 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.

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    More about this item

    Keywords

    Monotone comparative statics; Nonincreasing functions; Strategic substitutes; Parameterized games;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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