We propose an exchange economy evolutionary model with discrete time, in which there are two utility-maximizing groups of agents which differ in the preference structure. Assuming an evolutionary mechanism based on the relative utility values realized by the two kinds of agents, we analytically and numerically investigate the existence of equilibria, their stability, and possible phenomena of coexistence between groups, mainly in terms of the heterogeneity degree in the preference structure. We find that our system has two trivial equilibria, at which just one of the two groups is present, and possibly a nontrivial equilibrium, characterized by the coexistence of the two groups of agents. Such nontrivial equilibrium may be stable, attracting all trajectories, or unstable. In the latter case, interesting, periodic, or chaotic, dynamics arise. We prove that the nontrivial equilibrium emerges via a transcritical bifurcation and loses stability via a flip bifurcation, after which the coexistence between groups is oscillatory in nature, presenting a regular or irregular behavior. In order to better investigate the role of the heterogeneity degree parameter, we perform a bifurcation analysis considering different scenarios, characterized by a balanced or unbalanced endowment distribution of the two goods.

Naimzada, A., Pireddu, M. (2018). Complex Dynamics in an Evolutionary General Equilibrium Model. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2018, 1-13 [10.1155/2018/8471624].

Complex Dynamics in an Evolutionary General Equilibrium Model

Naimzada, A;Pireddu, M.
2018

Abstract

We propose an exchange economy evolutionary model with discrete time, in which there are two utility-maximizing groups of agents which differ in the preference structure. Assuming an evolutionary mechanism based on the relative utility values realized by the two kinds of agents, we analytically and numerically investigate the existence of equilibria, their stability, and possible phenomena of coexistence between groups, mainly in terms of the heterogeneity degree in the preference structure. We find that our system has two trivial equilibria, at which just one of the two groups is present, and possibly a nontrivial equilibrium, characterized by the coexistence of the two groups of agents. Such nontrivial equilibrium may be stable, attracting all trajectories, or unstable. In the latter case, interesting, periodic, or chaotic, dynamics arise. We prove that the nontrivial equilibrium emerges via a transcritical bifurcation and loses stability via a flip bifurcation, after which the coexistence between groups is oscillatory in nature, presenting a regular or irregular behavior. In order to better investigate the role of the heterogeneity degree parameter, we perform a bifurcation analysis considering different scenarios, characterized by a balanced or unbalanced endowment distribution of the two goods.
Articolo in rivista - Articolo scientifico
Heterogeneous preferences; exchange economy; evolution; coexistence; bifurcation; complex dynamics.
English
2018
2018
1
13
8471624
open
Naimzada, A., Pireddu, M. (2018). Complex Dynamics in an Evolutionary General Equilibrium Model. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2018, 1-13 [10.1155/2018/8471624].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/180458
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