Tâtonnement processes are usually interpreted as auctions, where a fictitious agent sets the prices until an equilibrium is reached and the trades are made. The main purpose of such processes is to explain how an economy comes to its equilibrium. It is well known that discrete time price adjustment processes may fail to converge and may exhibit periodic or even chaotic behavior. To avoid large price changes, a version of the discrete time tâtonnement process for reaching an equilibrium in a pure exchange economy based on a cautious updating of the prices has been proposed two decades ago. This modification leads to a one dimensional bimodal piecewise smooth map, for which we show analytically that degenerate bifurcations and border collision bifurcations play a fundamental role for the asymptotic behavior of the model.

Foroni, I., Avellone, A., & Panchuk, A. (2015). Sudden transition from equilibrium stability to chaotic dynamics in a cautious tâtonnement model. CHAOS, SOLITONS AND FRACTALS, 79, 105-115 [10.1016/j.chaos.2015.05.013].

Sudden transition from equilibrium stability to chaotic dynamics in a cautious tâtonnement model

Foroni, I
;
Avellone, A;
2015

Abstract

Tâtonnement processes are usually interpreted as auctions, where a fictitious agent sets the prices until an equilibrium is reached and the trades are made. The main purpose of such processes is to explain how an economy comes to its equilibrium. It is well known that discrete time price adjustment processes may fail to converge and may exhibit periodic or even chaotic behavior. To avoid large price changes, a version of the discrete time tâtonnement process for reaching an equilibrium in a pure exchange economy based on a cautious updating of the prices has been proposed two decades ago. This modification leads to a one dimensional bimodal piecewise smooth map, for which we show analytically that degenerate bifurcations and border collision bifurcations play a fundamental role for the asymptotic behavior of the model.
Articolo in rivista - Articolo scientifico
Asymptotic behaviors; Border collision bifurcation; Chaotic behaviors; Chaotic dynamics; Equilibrium stability; Piecewise-smooth map; Price adjustment; Pure exchanges
English
105
115
11
Foroni, I., Avellone, A., & Panchuk, A. (2015). Sudden transition from equilibrium stability to chaotic dynamics in a cautious tâtonnement model. CHAOS, SOLITONS AND FRACTALS, 79, 105-115 [10.1016/j.chaos.2015.05.013].
Foroni, I; Avellone, A; Panchuk, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/100423
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