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Adaptive Rational Equilibrium with Forward Looking Agents, fortcoming in International Journal of Economic Theory (IJET) 2006, special issue in honor of Jean-Michel Grandmont


  • Brock, W.A.

    (University of Wisconsin)

  • Dindo, P.D.E.

    () (Sant'Anna School of Advanced Studies, Pisa)

  • Hommes, C.H.

    () (Universiteit van Amsterdam)


Brock and Hommes (1997) introduce the concept of adaptive rational equilibrium dynamics (ARED)}, where agents choose between a costly rational expectation forecast and a cheap naive forecast, and the fractions using each of the two strategies evolve over time and are endogenously coupled to the market equilibrium price dynamics. In their setting agents are backward looking in the sense that strategy selection is based on experience measured by relative past realized profits. When the selection pressure to switch to the more profitable strategy is high, instability and complicated chaotic price fluctuations arise. In this paper we investigate the ARED with \textit{forward looking} agents, whose strategy selection is based upon expected profits. Our findings suggest that forward looking behavior dampens the amplitude of price fluctuations, but local instability of the steady state remains. The global dynamics depends upon how sophisticated the forward looking behavior is. With perfectly forward looking agents prices converge to a stable 2-cycle, while with forward looking agents who are boundedly rational concerning their estimate of expected profits, small amplitude chaotic price fluctuations may arise. We also establish an equivalence relationship between a heterogeneous agent model with switching of strategies and a representative agent framework, where the representative agent optimally chooses between the benefits of a high quality forecasts and the associated information gathering costs. To an outside observer it is impossible to distinguish between the two.

Suggested Citation

  • Brock, W.A. & Dindo, P.D.E. & Hommes, C.H., 2005. "Adaptive Rational Equilibrium with Forward Looking Agents, fortcoming in International Journal of Economic Theory (IJET) 2006, special issue in honor of Jean-Michel Grandmont," CeNDEF Working Papers 05-15, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:05-15

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    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    3. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    4. Camerer, Colin F. & Ho, Teck H. & Chong, Juin-Kuan., 2000. "Sophisticated EWA Learning and Strategic Teaching in Repeated Games," Working Papers 1087, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Bullard James, 1994. "Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 64(2), pages 468-485, December.
    6. Tuinstra, Jan, 2003. "Beliefs equilibria in an overlapping generations model," Journal of Economic Behavior & Organization, Elsevier, vol. 50(2), pages 145-164, February.
    7. de Fontnouvelle, Patrick, 2000. "Information Dynamics In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 139-169, June.
    8. Goeree, Jacob K. & Hommes, Cars H., 2000. "Heterogeneous beliefs and the non-linear cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 761-798, June.
    9. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    10. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    11. Maciej K. Dudek, 2004. "Expectation Formation and Endogenous Fluctuations in Aggregate Demand," Econometric Society 2004 Latin American Meetings 103, Econometric Society.
    12. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    13. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    14. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    15. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics,in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
    16. Evans, George W & Ramey, Garey, 1992. "Expectation Calculation and Macroeconomic Dynamics," American Economic Review, American Economic Association, vol. 82(1), pages 207-224, March.
    17. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 287-321, September.
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