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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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    1. Harris, Christopher, 1985. "A characterisation of the perfect equilibria of infinite horizon games," Journal of Economic Theory, Elsevier, vol. 37(1), pages 99-125, October.
    2. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
    3. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    4. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    5. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    6. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    7. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    9. Hellwig, Martin & Leininger, Wolfgang, 1987. "On the existence of subgame-perfect equilibrium in infinite-action games of perfect information," Journal of Economic Theory, Elsevier, vol. 43(1), pages 55-75, October.
    10. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    11. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    12. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    13. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    14. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    15. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-544, May.
    16. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
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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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