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Mixed Equilibria in Games of Strategic Complements are Unstable

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Listed:
  • Federico Echenique
  • Aaron Edlin

Abstract

In games with strict strategic complementarities, properly mixed Nash equilibria--equilibria that are not in pure strategies--are unstable for a broad class of learning dynamics.
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Suggested Citation

  • Federico Echenique & Aaron Edlin, 2001. "Mixed Equilibria in Games of Strategic Complements are Unstable," Levine's Working Paper Archive 563824000000000161, David K. Levine.
    • Handle: RePEc:cla:levarc:563824000000000161
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    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    3. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    5. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    7. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    8. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    9. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
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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," 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. Amir, Rabah & Garcia, Filomena & Knauff, Malgorzata, 2010. "Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1968-1986, September.
    4. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
    5. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    6. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.
    7. Rabah Amir, 2005. "Supermodularity and Complementarity in Economics: An Elementary Survey," Southern Economic Journal, John Wiley & Sons, vol. 71(3), pages 636-660, January.
    8. 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.
    9. Ewerhart, Christian & Sun, Guang-Zhen, 2024. "The n-player Hirshleifer contest," Games and Economic Behavior, Elsevier, vol. 143(C), pages 300-320.
    10. Arora, Gaurav, 2017. "Studies on factors affecting the evolution of agroecosystems in the Dakotas," ISU General Staff Papers 201701010800006258, Iowa State University, Department of Economics.
    11. Amir, Rabah & Halmenschlager, Christine & Jin, Jim, 2011. "R&D-induced industry polarization and shake-outs," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 386-398, July.
    12. Echenique, Federico & Edlin, Aaron, 2004. "Mixed equilibria are unstable in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 118(1), pages 61-79, September.
    13. Arora, Gaurav & Feng, Hongli & Hennessy, David A. & Loesch, Charles R. & Kvas, Susan, 2021. "The impact of production network economies on spatially-contiguous conservation– Theoretical model with evidence from the U.S. Prairie Pothole Region," Journal of Environmental Economics and Management, Elsevier, vol. 107(C).
    14. Lu Yu, 2024. "Nash equilibria of quasisupermodular games," Papers 2406.13783, arXiv.org.

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    More about this item

    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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