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Extensive-form games and strategic complementarities

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  • Federico Echenique

    (UC Berkeley and Universidad de la Republica)

Abstract

(less than 25 lines) I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a non-empty, complete lattice. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. The correspondence has a natural interpretation. My results are limited because extensive-form games of strategic complementarities turn out---surprisingly---to be a very restrictive class of games.

Suggested Citation

  • Federico Echenique, 2000. "Extensive-form games and strategic complementarities," Game Theory and Information 0004005, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0004005
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    References listed on IDEAS

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    Cited by:

    1. Tarun Sabarwal & Hoa VuXuan, 2018. "Two Stage 2 × 2 Games With Strategic Substitutes and Strategic Heterogeneity," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201902, University of Kansas, Department of Economics.
    2. Mathevet, Laurent & Steiner, Jakub, 2013. "Tractable dynamic global games and applications," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2583-2619.
    3. Renou, Ludovic, 2009. "Commitment games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 488-505, May.
    4. Laurent Mathevet & Jakub Steiner, 2012. "Sand in the Wheels: A Dynamic Global-Game Approach," CERGE-EI Working Papers wp459, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    5. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
    6. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    7. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    8. Mensch, Jeffrey, 2020. "On the existence of monotone pure-strategy perfect Bayesian equilibrium in games with complementarities," Journal of Economic Theory, Elsevier, vol. 187(C).
    9. Feng, Yue & Sabarwal, Tarun, 2020. "Strategic complements in two stage, 2 × 2 games," Journal of Economic Theory, Elsevier, vol. 190(C).
    10. Xavier Vives, 2009. "Strategic complementarity in multi-stage games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 151-171, July.
    11. Lambertini, Luca & Mantovani, Andrea, 2006. "Identifying reaction functions in differential oligopoly games," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 252-271, December.
    12. Yue Feng & Tarun Sabarwal, 2018. "Strategic Complements in Two Stage, 2 × 2 Games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201801, University of Kansas, Department of Economics.
    13. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
    14. Li, Jian & Zhou, Junjie & Chen, Ying-Ju, 2021. "The Limit of Targeting in Networks," ISU General Staff Papers 202112081957590000, Iowa State University, Department of Economics.
    15. Vives, Xavier, 2006. "Strategic Complementarities in Multi-Stage Games," CEPR Discussion Papers 5583, C.E.P.R. Discussion Papers.
    16. Nobuyuki Hanaki & Ali I. Ozkes, 2023. "Strategic environment effect and communication," Experimental Economics, Springer;Economic Science Association, vol. 26(3), pages 588-621, July.
    17. 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.
    18. Li, Jian & Zhou, Junjie & Chen, Ying-Ju, 2022. "The limit of targeting in networks," Journal of Economic Theory, Elsevier, vol. 201(C).
    19. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    20. Koch, Caleb M., 2019. "Index-wise comparative statics," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 35-41.

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    JEL classification:

    • 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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