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A characterization of strategic complementarities

Author

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  • Federico Echenique

Abstract

I characterize games for which there is an order on strategies such that the game has strategic complementarities. I prove that, with some qualifications, games with a unique equilibrium have complementarities if and only if Cournot best-response dynamics has no cycles; and that all games with multiple equi- libria have complementarities. As applications of my results, I show: 1. That generic 2X2 games either have no pure-strategy equilibria, or have complementarities. 2. That generic two-player finite ordinal potential games have complementarities.

Suggested Citation

  • Federico Echenique, 2001. "A characterization of strategic complementarities," Documentos de Trabajo (working papers) 0501, Department of Economics - dECON.
    • Handle: RePEc:ude:wpaper:0501
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    File URL: https://hdl.handle.net/20.500.12008/1935
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    Cited by:

    1. AMIR, Rabah & GARCIA, Filomena & KNAUFF, Malgorzata, 2006. "Endogenous heterogeneity in strategic models: symmetry-breaking via strategic substitutes and nonconcavities," LIDAM Discussion Papers CORE 2006008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Cao, Zhigang & Chen, Xujin & Qin, Cheng-Zhong & Wang, Changjun & Yang, Xiaoguang, 2018. "Embedding games with strategic complements into games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 45-51.
    3. Swank, Otto H. & Visser, Bauke, 2023. "Committees as active audiences: Reputation concerns and information acquisition," Journal of Public Economics, Elsevier, vol. 221(C).
    4. 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.
    5. Jens Gudmundsson & Jens Leth Hougaard, 2025. "Smart contracts and reaction-function games," Papers 2506.14413, arXiv.org, revised Jan 2026.
    6. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
    7. Amir, Rabah & Lazzati, Natalia, 2016. "Endogenous information acquisition in Bayesian games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 163(C), pages 684-698.
    8. Amir, Rabah, 2005. "Ordinal versus cardinal complementarity: The case of Cournot oligopoly," Games and Economic Behavior, Elsevier, vol. 53(1), pages 1-14, October.
    9. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    10. Tesoriere, Antonio, 2008. "Endogenous R&D symmetry in linear duopoly with one-way spillovers," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 213-225, May.
    11. Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2015. "Political Economy in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1038-1086.
    12. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    13. Tang, Pingzhong & Lin, Fangzhen, 2011. "Two equivalence results for two-person strict games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 479-486, March.
    14. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    15. 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.
    16. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    17. TESORIERE, Antonio, 2005. "Endogenous R&D symmetry in linear duopoly with one-way spillovers," LIDAM Discussion Papers CORE 2005045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.
    19. Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino & Vladimir Oudalov, 2016. "Sufficient conditions for the existence of Nash equilibria in bimatrix games in terms of forbidden $$2 \times 2$$ 2 × 2 subgames," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1111-1131, November.
    20. Jeremy Fox & Natalia Lazzati, 2013. "Identification of discrete choice models for bundles and binary games," CeMMAP working papers CWP04/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. 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.
    22. Takahashi, Satoru, 2008. "The number of pure Nash equilibria in a random game with nondecreasing best responses," Games and Economic Behavior, Elsevier, vol. 63(1), pages 328-340, May.
    23. 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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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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