Chaotic tatonnement

Bala, Venkatesh; Majumdar, Mukul

doi:10.1007/bf01212469

Cited by 50 publications

(35 citation statements)

References 14 publications

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“…by Arrow et al(1959), Scarf (1960) and Arrow and Hahn (1971), and in discrete time e.g. by Saari (1985), Bala and Majumdar (1992), Day and Pianigiani (1991), Weddepohl (1995), Goeree et al (1998) and Tuinstra ( , 2000. In our asset pricing setting, an advantage of the simple price adjustment rule (12) is that the model remains analytically tractible and reduces to a 2-dimensional system.…”

Section: The Modelmentioning

confidence: 99%

“…Chapter 2). 4 For the system we are considering, the fundamental steady state E becomes a saddle point after the pitchfork bifurcation in the symmetric case z s = 0 or after the transcritical bifurcation in the asymmetric case z s > 0. Figures 7c and 7g show that, as the intensity of choice β increases, a homoclinic bifurcation occurs, between the right respectively the left branch of the unstable manifold W u (E) of and the stable manifold W s (E) of the fundamental steady states.…”

Section: Strange Attractorsmentioning

confidence: 99%

See 1 more Smart Citation

A robust rational route to randomness in a simple asset pricing model

Hommes

Huang

Wang

2005

Journal of Economic Dynamics and Control

136

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We investigate asset pricing dynamics in an adaptive evolutionary asset pricing model with fundamentalists, trend followers and a market maker. Agents can choose between a fundamentalist strategy at positive information cost or choose a trend following strategy for free. Price adjustment is proportional to the excess demand in the asset market. Agents asynchronously update their strategy according to realized net profits in the recent past. As agents become more sensitive to differences in strategy performance, the fundamental steady state becomes unstable and multiple steady states may arise. As the traders' sensitivity to differences in fitness increases, a bifurcation route to chaos sets in due to homoclinic bifurcations of stable and unstable manifolds of the fundamental steady state. JEL classification: E32, G12, D84Keywords: heterogeneous beliefs, bounded rationality, market maker scenario, bifurcations, chaos. * We would like to thank Florian Wagener for stimulating discussions.We also would like to thank two anonymous referees and the editor Ken Judd for helpful comments on an earlier draft.

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Section: The Modelmentioning

confidence: 99%

Section: Strange Attractorsmentioning

confidence: 99%

A robust rational route to randomness in a simple asset pricing model

Hommes

Huang

Wang

2005

Journal of Economic Dynamics and Control

136

View full text Add to dashboard Cite

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“…The two other equilibria x * = ± θ are stable for θ > 0, as illustrated in our Bala (1997) explains how pitchfork bifurcation occurs in the tatonnement process. Chaos also can exist in the tatonnement process, as shown in Bala and Majumdar (1992).…”

Section: Pitchfork Bifurcationsmentioning

confidence: 99%

Singularity bifurcations

Barnett

2006

Journal of Macroeconomics

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Abstract:Euler equation models represent an important class of macroeconomic systems. Our ongoing research (He and Barnett (2003)) on the Leeper and Sims (1994) Euler equations macroeconometric model is revealing the existence of singularity-induced bifurcations, when the model's parameters are within a confidence region about the parameter estimates. Although known to engineers, singularity bifurcation has not previously been seen in the economics literature. Knowledge of the nature of singularity-induced bifurcations is likely to become important in understanding the dynamics of modern macroeconometric models. This paper explains singularityinduced bifurcation, its nature, and its identification and contrasts this class of bifurcations with the more common forms of bifurcation we have previously encountered within the parameter space of the Bergstrom and Wymer (1976) continuous time macroeconometric model of the UK economy.

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“…The papers by Arrow and Hurwicz (1958), Arrow and Hahn (1971), and Negishi (1958) have proved that the continuous tâtonnement process converges to the unique equilibrium price under global gross substitutability. Recent major contributions to the tâtonnemnt process have been devoted to instability of discrete tâtonnemnt process, The papers by Bala and Majumdar (1992), Day and Pianigiani (1991), Day (1994) and Mukherji (1999) show that the discrete tâtonnemnt process may lead to chaotic dynamics under global gross substitutability. Further, Goeree et al (1998), Junistra (1997, 1999, Saari (1985), and Weddepohl (1995) show that the discrete tâtonnement processes become unstable and exhibit chaos as the speed of price adjustment increases.…”

Section: Introductionmentioning

confidence: 99%