Fashion cycle dynamics induced by agents' heterogeneity for generic bell-shaped attractiveness functions

Abstract

We extend the exchange economy evolutionary discrete-time model with heterogeneous agents introduced in 'Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences', by A. Naimzada and M. Pireddu, appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 055907 (2018), by considering generic bell-shaped attractiveness functions for the two groups of agents, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. The reproduction level of a group is related to its attractiveness degree, which depends on its social visibility level, determined by the consumption choices of the agents in that group. We investigate the asymptotic heterogeneity among agents, finding that the global dynamics may differ according to the chosen functional form for the attractiveness. Nonetheless, the model is still able to reproduce the recurrent dynamic behaviour typical of the fashion cycle.

A General Equilibrium Evolutionary Model with Generic Utility Functions and Generic Bell-Shaped Attractiveness Maps, Generating Fashion Cycle Dynamics

“…In the past decades, some dynamical models have been proposed to give a formal representation of the fashion cycle (see, for instance, Bianchi, 2002;Caulkins et al, 2007;Coelho and McClure, 1993;Corneo and Jeanne, 1999;Di Giovinazzo and Naimzada, 2015;Frijters, 1998;Gardini et al, 2018;Karni and Schmeidler, 1990;Matsuyama, 1991;Pesendorfer, 1995;Zhang, 2016Zhang, , 2017, i.e., of the oscillatory behavior of the variable describing the consumed or purchased amount of a certain good, characterized by booms and busts. Differently from the above mentioned works, following the line of research started in Chang and Stauber (2009) and further developed in Naimzada and Pireddu (2016, 2018a, 2018b, 2018c, 2018d, 2019b, we here present an evolutive general equilibrium model, in which we may investigate the combined effects of the price formation mechanism and of the population share updating mechanism, that describes the socio-economic interaction of two groups of agents exhibiting both bandwagon and snob behaviors. However, unlike the previous contributions, in which only Cobb-Douglas utility functions were considered, we now allow the agents' utility functions to vary in a suitable set of maps.…”

The First Fundamental Theorem of Welfare in a General Equilibrium Evolutionary Setting

“…We remark that, in order not to overburden notation and terminology, although a * is not part of the market equilibrium vector introduced in Definition 2.2, we call the objects described in Definition 2.3 (market stationary) equilibria, and we use the symbol * even for the shares. In fact, as done in Naimzada and Pireddu (2018, 2019a, 2019b, when for all population shares each economy admits a unique market equilibrium, it is possible to identify market stationary equilibria just with the population share a * , since it univocally determines all other equilibrium components. Namely, according to what explained in Subsection 2.1, when dealing e.g.…”

“…Thanks to the combined action of the price mechanism and of the share updating rule, the model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts both in the agents' consumption choices and in the population shares. We recall that the setting in Naimzada and Pireddu (2019b) is a generalization of that in Naimzada and Pireddu (2019a), in which only Cobb-Douglas utility functions were considered. The context in Naimzada and Pireddu (2019a) is in turn an extension of the framework in Naimzada and Pireddu (2018), where just one particular formulation of the attractiveness was taken into account.…”

“…We recall that the setting in Naimzada and Pireddu (2019b) is a generalization of that in Naimzada and Pireddu (2019a), in which only Cobb-Douglas utility functions were considered. The context in Naimzada and Pireddu (2019a) is in turn an extension of the framework in Naimzada and Pireddu (2018), where just one particular formulation of the attractiveness was taken into account. The remaider of the paper is organized as follows.…”

Complexity Analysis of Pricing in a Multichannel Supply Chain with Spillovers from Online to Offline Sales

“…Taking the input of a retailing service into account, Ma et al [12] investigated a dual-channel dynamic game and explored the stability of the equilibrium point and further made a discussion about the effects of the adjustment speed on the complexity of the game system and the market performance. In addition, for dynamic analysis, Naimzada and Pireddu [13] explored the dynamic behavior of the fashion cycle by investigating the asymptotic heterogeneity among agents and found that the global dynamics may differ according to the chosen functional form for the attractiveness. Naimzada and Pireddu [14] also examined the globally eductive stability of a Muthian cobweb model in a profit-based evolutionary setting, assuming that agents face heterogeneous information costs.…”