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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 equilibria have complementarities. This is a negative result because it implies that the predictive power of complementarities alone is very weak. As an application of my results I show that generic 2 X 2 games either have no pure-strategy equilibria, or are GSC.

Suggested Citation

• Federico Echenique, 2001. "A Characterization of Strategic Complementarities," GE, Growth, Math methods 0103001, University Library of Munich, Germany.
• Handle: RePEc:wpa:wuwpge:0103001
Note: 19 pages, Acrobat .pdf
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File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0103/0103001.pdf

References listed on IDEAS

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1. Echenique, Federico, 2002. "Finding All Equilibria," Working Papers 1153, California Institute of Technology, Division of the Humanities and Social Sciences.
2. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
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13. Federico Echenique, 2003. "The equilibrium set of two-player games with complementarities is a sublattice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 903-905, November.
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Citations

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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," CORE Discussion Papers 2006008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
2. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
3. 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.
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. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
6. 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.
7. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, Southern Economic Association, vol. 71(3), pages 636-660, January.
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. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. TESORIERE, Antonio, 2005. "Endogenous R&D symmetry in linear duopoly with one-way spillovers," CORE Discussion Papers 2005045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
15. Berger, Ulrich, 2009. "The convergence of fictitious play in games with strategic complementarities: A Comment," MPRA Paper 20241, University Library of Munich, Germany.
16. 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.

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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