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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 8471624, 13 pages
https://doi.org/10.1155/2018/8471624
Research Article

Complex Dynamics in an Evolutionary General Equilibrium Model

1Department of Economics, Management and Statistics, University of Milano-Bicocca, U6 Building, Piazza dell’Ateneo Nuovo 1, 20126 Milano, Italy
2Department of Mathematics and Its Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano, Italy

Correspondence should be addressed to Marina Pireddu; ti.biminu@udderip.aniram

Received 29 August 2017; Revised 2 December 2017; Accepted 10 December 2017; Published 16 January 2018

Academic Editor: Ricardo López-Ruiz

Copyright © 2018 Ahmad Naimzada and Marina Pireddu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.