Chaotic social interaction via endogenous reactivity

Abstract

We propose a framework to analyse the dynamical process of decision and opinion formation of two economic homogeneous and boundedly rational agents that interact and learn from each other over time. The decisional process described in our model is an adaptive adjustment mechanism in which two agents take into account the difference between their own opinion and the opinion of the other agent. The smaller that difference, the larger the weight given to the comparison of the opinions. We assume that if the distance between the two opinions is larger than a given threshold, then there is no interaction and the agents do not change their opinion anymore. Introducing an auxiliary variable describing the distance between the opinions, we obtain a one-dimensional map for which we investigate, mainly via analytical tools, the stability of the steady states, their bifurcations, as well as the existence of chaotic dynamics and multistability phenomena.

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

“…Thus, both in [28,36] a sort of bandwagon behaviour can be observed, while the snob attitude can be witnessed in [28] only. Moreover, non-constant pursuit strategies in [28] and the endogenous reactivity assumption in [36] lead to nonlinear systems, in which chaotic dynamics can emerge. Finally, we stress that, rather than considering stable preferences as we do, it is possible to deal with preference adjusting consumers, like in [22][23][24][25][26]33], where cycles are found in a model with agents having globally interdependent preferences.…”

“…On the other hand, differently from those papers, the binary choice here occurs between preference structures that characterize the two groups of agents, which are embedded in a general equilibrium framework where a price mechanism operates. Two further works which bear some resemblance to our setting are [28,36]. Namely, in [28] a class of pursuit problems is proposed, in which a decision-maker reacts in an adaptive manner to the choices of the other agent, which tries to run away, in view of reducing the distance between them.…”

“…Namely, in [28] a class of pursuit problems is proposed, in which a decision-maker reacts in an adaptive manner to the choices of the other agent, which tries to run away, in view of reducing the distance between them. In [36], this time in an opinion dynamics framework, agents look for a mediation between their positions in an adaptive perspective. Thus, both in [28,36] a sort of bandwagon behaviour can be observed, while the snob attitude can be witnessed in [28] only.…”

“…In [36], this time in an opinion dynamics framework, agents look for a mediation between their positions in an adaptive perspective. Thus, both in [28,36] a sort of bandwagon behaviour can be observed, while the snob attitude can be witnessed in [28] only. Moreover, non-constant pursuit strategies in [28] and the endogenous reactivity assumption in [36] lead to nonlinear systems, in which chaotic dynamics can emerge.…”