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Discrete beliefs space and equilibrium: a cautionary note

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  • Michele Berardi

    (The University of Manchester)

Abstract

Bounded rationality requires assumptions about ways in which rationality is constrained and agents form their expectations. Evolutionary schemes have been used to model beliefs dynamics, with agents choosing endogenously among a limited number of beliefs heuristics according to their relative performance. This work shows that arbitrarily constraining the beliefs space to a finite (small) set of possibilities can generate artificial equilibria that can be stable under evolutionary dynamics. Only when “enough” heuristics are available are beliefs in equilibrium not artificially constrained. I discuss these findings in light of an alternative approach to modelling beliefs dynamics, namely, adaptive learning.

Suggested Citation

  • Michele Berardi, 2021. "Discrete beliefs space and equilibrium: a cautionary note," Journal of Evolutionary Economics, Springer, vol. 31(2), pages 505-532, April.
    • Handle: RePEc:spr:joevec:v:31:y:2021:i:2:d:10.1007_s00191-020-00689-1
    DOI: 10.1007/s00191-020-00689-1
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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    3. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    4. Berardi, Michele, 2015. "On the fragility of sunspot equilibria under learning and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 251-265.
    5. Evans, George W. & Honkapohja, Seppo & Mitra, Kaushik, 2009. "Anticipated fiscal policy and adaptive learning," Journal of Monetary Economics, Elsevier, vol. 56(7), pages 930-953, October.
    6. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    7. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
    8. Branch, William A., 2002. "Local convergence properties of a cobweb model with rationally heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 63-85, November.
    9. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    10. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    11. Aoki, Masanao, 2002. "Open models of share markets with two dominant types of participants," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 199-216, October.
    12. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    13. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk‐Hoppé, 2002. "Market Selection Of Financial Trading Strategies: Global Stability," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 329-339, October.
    14. Mikhail Anufriev & Cars Hommes, 2012. "Evolutionary Selection of Individual Expectations and Aggregate Outcomes in Asset Pricing Experiments," American Economic Journal: Microeconomics, American Economic Association, vol. 4(4), pages 35-64, November.
    15. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    16. George W. Evans & Seppo Honkapohja, 2003. "Expectations and the Stability Problem for Optimal Monetary Policies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(4), pages 807-824.
    17. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    18. Berardi, Michele, 2007. "Heterogeneity and misspecifications in learning," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3203-3227, October.
    19. Diks, C.G.H. & Weide, R. van der, 2002. "Continuous Beliefs Dynamics," CeNDEF Working Papers 02-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    20. Berardi, Michele, 2009. "Heterogeneous expectations, sunspot equilibria and their fragility," Economics Letters, Elsevier, vol. 105(3), pages 276-279, December.
    21. George W. Evans, 2001. "Expectations in Macroeconomics. Adaptive versus Eductive Learning," Revue Économique, Programme National Persée, vol. 52(3), pages 573-582.
    22. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    23. Branch, William A. & Evans, George W., 2006. "Intrinsic heterogeneity in expectation formation," Journal of Economic Theory, Elsevier, vol. 127(1), pages 264-295, March.
    24. Anufriev, Mikhail & Assenza, Tiziana & Hommes, Cars & Massaro, Domenico, 2013. "Interest Rate Rules And Macroeconomic Stability Under Heterogeneous Expectations," Macroeconomic Dynamics, Cambridge University Press, vol. 17(8), pages 1574-1604, December.
    25. Branch, William & McGough, Bruce, 2016. "Heterogeneous beliefs and trading inefficiencies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 786-818.
    26. Diks, C.G.H. & Weide, R. van der, 2003. "Heterogeneity as a natural source of randomness," CeNDEF Working Papers 03-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    27. Cees Diks & Roy van der Weide, 2003. "Heterogeneity as a Natural Source of Randomness," Tinbergen Institute Discussion Papers 03-073/1, Tinbergen Institute.
    28. Sethi, Rajiv & Franke, Reiner, 1995. "Behavioural Heterogeneity under Evolutionary Pressure: Macroeconomic Implications of Costly Optimisation," Economic Journal, Royal Economic Society, vol. 105(430), pages 583-600, May.
    29. Paul Grauwe, 2011. "Animal spirits and monetary policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 423-457, June.
    30. 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.
    31. Anna Agliari & Domenico Massaro & Nicolò Pecora & Alessandro Spelta, 2017. "Inflation Targeting, Recursive Inattentiveness, and Heterogeneous Beliefs," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(7), pages 1587-1619, October.
    32. Branch, William A. & McGough, Bruce, 2008. "Replicator dynamics in a Cobweb model with rationally heterogeneous expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 65(2), pages 224-244, February.
    33. Marimon, Ramon, 1993. "Adaptive learning, evolutionary dynamics and equilibrium selection in games," European Economic Review, Elsevier, vol. 37(2-3), pages 603-611, April.
    34. Guse, Eran A., 2010. "Heterogeneous expectations, adaptive learning, and evolutionary dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 74(1-2), pages 42-57, May.
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    More about this item

    Keywords

    Expectations; Evolutionary dynamics; Learning; Equilibrium;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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