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Stability, chaos and multiple attractors: a single agent makes a difference. (English) Zbl 1178.91105
Summary: This paper provides an example in which a slight behavioral heterogeneity may fundamentally change the dynamical properties of a nonlinear cobweb market with a quadratic cost function and an isoelastic demand function. We consider two types of producers; cautious adapters and naive optimizers. In a market of naive optimizers a single cautious adapter stabilizes the otherwise exploding market. In a market of cautious adapters a single naive optimizer may destabilize the market; without him there exists at most one periodic attractor in the market but with him there may appear many (and even infinitely many) coexisting periodic attractors.

91B55Economic dynamics
37N40Dynamical systems in optimization and economics
37D45Strange attractors, chaotic dynamics
Full Text: DOI
[1] Axelrod, R.: The evolution of cooperation. (1984) · Zbl 1225.92037
[2] Barinci, J. P.: Factors substitutability, heterogeneity and endogenous fluctuations in a finance constrained economy. Economic theory 17, 181-195 (2001) · Zbl 0978.91059
[3] Bomfin, A.: Heterogeneous forecasts and aggregate dynamics. Journal of monetary economics 47, 145-161 (2001)
[4] Brock, W. A.; Hommes, C. H.: A rational route to randomness. Econometrica 65, 1059-1095 (1997) · Zbl 0898.90042
[5] Cardak, B. A.: Heterogeneous preferences, education expenditures and income distribution. Economic record 75, 63-76 (1999)
[6] Chiarella, C.: The dynamics of speculative behavior. Annals of operations research 37, 101-123 (1992) · Zbl 0777.90008
[7] Chiu, W. H.: Income inequality, human capital accumulation and economic performance. Economic journal 108, 44-59 (1998)
[8] Cooper, R.: Business cyclestheory, evidence and policy implications. Scandinavian journal of economics 100, 213-237 (1998) · Zbl 0908.90042
[9] Day, R. H.; Huang, W.: Bulls, bears and market sheep. Journal of economic behavior and organization 14, 299-329 (1990)
[10] Delli-Gatti, D., Gallegati, M., Kirman, A. (Eds.), 2000. Interaction and market structure: essays on heterogeneity in economics, Lecture Notes in Economics and Mathematical Systems, Vol. 484. Springer, Berlin. · Zbl 0937.00030
[11] Den-Haan, W. J.: The importance of the number of different agents in a heterogeneous asset-pricing model. Journal of economic dynamics and control 25, 721-746 (2001) · Zbl 0963.91051
[12] Franke, R.; Nesemann, T.: Two destabilizing strategies May be jointly stabilizing. Journal of economics 69, 1-18 (1999) · Zbl 0992.91019
[13] Gallegati, M., Kirman, A. (Eds.), 2000. Beyond the Representative Agent. Elgar, Cheltenham.
[14] Gaunersdorfer, A.: Endogenous fluctuations in a simple asset pricing model with heterogeneous agents. Journal of economic dynamics and control 24, 799-831 (2000) · Zbl 0949.91011
[15] Goeree, J. K.; Hommes, C. H.: Heterogeneous beliefs and the non-linear cobweb model. Journal of economic dynamics and control 24, 761-798 (2000) · Zbl 0945.91039
[16] Kirman, A., Zimmermann, J.-B. (Eds.), 2001. Economics with heterogeneous interacting agents, Lecture Notes in Economics and Mathematical Systems, Vol. 503. Springer, Berlin. · Zbl 0964.00027
[17] Lucas, R. E.: Adaptive behavior and economic theory. Journal of business 59, 401-426 (1986)
[18] Lux, T.: Herd behavior, bubbles and crashes. Economic journal 105, 881-896 (1995)
[19] Lux, T.; Marchesi, M.: Volatility clustering in financial marketsa micro-simulation of interacting agents. International journal of theoretical and applied finance 3, 675-702 (2000) · Zbl 0967.91072
[20] Mora, L.; Viana, M.: Abundance of strange attractors. Acta Mathematica 171, 1-71 (1993) · Zbl 0815.58016
[21] Onozaki, T.; Sawada, K.: Complementary analysis of a nonlinear cobweb model with adaptive production adjustment. Journal of asahikawa university 51, 58-64 (2001)
[22] Onozaki, T.; Sieg, G.; Yokoo, M.: Complex dynamics in a cobweb model with adaptive production adjustment. Journal of economic behavior and organization 41, 101-115 (2000)
[23] Palis, J.; Takens, F.: Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations. (1993) · Zbl 0790.58014
[24] Robinson, C.: Bifurcation to infinitely many sinks. Communications in mathematical physics 90, 433-459 (1983) · Zbl 0531.58035
[25] Sarte, P. D.: Progressive taxation and income inequality in dynamic competitive equilibrium. Journal of public economics 66, 145-171 (1997)
[26] Singer, D.: Stable orbits and bifurcations of maps of the interval. SIAM journal of applied mathematics 35, 260-267 (1978) · Zbl 0391.58014
[27] Takens, F.: Abundance of generic homoclinic tangencies in real-analytic families of diffeomorphisms. Boletim da sociedade brasileira de matemática 22, 191-214 (1992) · Zbl 0772.58037
[28] De Vilder, R.: Complicated endogenous business cycles under Gross substitutability. Journal of economic theory 71, 416-442 (1996) · Zbl 0877.90021
[29] Yorke, J. A.; Alligood, K. T.: Cascades of period-doubling bifurcationsa prerequisite for horseshoes. Bulletin of American mathematical society 9, 319-322 (1983) · Zbl 0541.58039