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Expectational coordination in a class of economic models: Strategic substitutabilities versus strategic complementarities

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  • Roger Guesnerie

    (Chaire Théorie économique et organisation sociale - CdF (institution) - Collège de France, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Pedro Jara-Moroni

    (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, Departamento de Economía - Universidad de Chile)

Abstract

We consider an economic model that features: 1. a continuum of agents 2. an aggregate state of the world over which agents have an infinitesimal influence. We first propose a review, based on work by Jara (2007), of the connections between the eductive viewpoint that puts emphasis on Strongly Rational Expectations equilibrium and the standard game-theoretical rationalizability concepts. We explore the scope and limits of this connection depending on whether standard rationalizability versus point-rationalizability, or the local versus the global viewpoint, are concerned. In particular, we define and characterize the set of Point-Rationalizable States and prove its convexity. Also, we clarify the role of the heterogeneity of beliefs in general contexts of expectational coordination (see Evans and Guesnerie, 2005). Then, as in the case of strategic complementarities the study of some best response mapping is a key to the analysis, in the case of unambiguous strategic substitutabilities the study of some second iterate, and of the corresponding two-period cycles, allows to describe the point-rationalizable states. We provide application in microeconomic and macroeconomic contexts.

Suggested Citation

  • Roger Guesnerie & Pedro Jara-Moroni, 2007. "Expectational coordination in a class of economic models: Strategic substitutabilities versus strategic complementarities," PSE Working Papers halshs-00587837, HAL.
  • Handle: RePEc:hal:psewpa:halshs-00587837
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    Cited by:

    1. William Branch & George Evans, 2011. "Monetary policy and heterogeneous expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 365-393, June.
    2. Roger Guesnerie, 2009. "Macroeconomic and Monetary Policies from the Eductive Viewpoint," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 6, pages 171-202, Central Bank of Chile.
    3. Gabriel Desgranges & Stéphane Gauthier, 2013. "Asymmetric information and rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 789-804, November.
    4. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    5. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    6. George W Evans & Roger Guesnerie & Bruce McGough, 2019. "Eductive Stability in Real Business Cycle Models," The Economic Journal, Royal Economic Society, vol. 129(618), pages 821-852.
    7. William Branch & George Evans, 2011. "Monetary policy and heterogeneous expectations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 365-393, June.
    8. Harrison, Rodrigo & Jara-Moroni, Pedro, 2015. "A dominance solvable global game with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 1-11.
    9. Qiao, Lei & Yu, Haomiao & Zhang, Zhixiang, 2016. "On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization," Games and Economic Behavior, Elsevier, vol. 99(C), pages 89-98.
    10. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
    11. Mordecai Kurz, 2011. "Symposium: on the role of market belief in economic dynamics, an introduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 189-204, June.
    12. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.
    13. Shurojit Chatterji & Atsushi Kajii, 2020. "Decentralizability of efficient allocations with heterogenous forecasts," Working Papers on Central Bank Communication 016, University of Tokyo, Graduate School of Economics.
    14. Mordecai Kurz & Maurizio Motolese, 2011. "Diverse beliefs and time variability of risk premia," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 293-335, June.
    15. Khan, Mohammed Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2017. "On the equivalence of large individualized and distributionalized games," Theoretical Economics, Econometric Society, vol. 12(2), May.
    16. Shurojit Chatterji & Atsushi Kajii, 2021. "Decentralizability of efficient allocations with heterogenous forecasts," Working Papers on Central Bank Communication 031, University of Tokyo, Graduate School of Economics.
    17. Rabah Amir, 2019. "Supermodularity and Complementarity in Economic Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 487-496, April.
    18. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    19. George W Evans & Roger Guesnerie & Bruce McGough, 2019. "Eductive Stability in Real Business Cycle Models," Economic Journal, Royal Economic Society, vol. 129(618), pages 821-852.
    20. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
    21. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).

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    More about this item

    Keywords

    expectational coordination; rational expectations; iterative expectational stability; eductive stability; strong rationality; strategic complementarities; strategic substitutabilities;
    All these keywords.

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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