Statistical Economics on Multi-Variable Layered Networks

TL;DR

This paper introduces a multi-layered network framework inspired by statistical mechanics to model complex economic systems, capturing interactions among diverse agent variables across different social layers, revealing emergent herding phenomena.

Contribution

It develops a novel multi-layered network model with coupled variables of different types, demonstrating emergent collective behavior in economic systems.

Findings

Coupled layers exhibit herding behavior absent in individual layers.

The framework captures contagion effects across different social variables.

Emergent phenomena arise from the interaction of diverse agent variables.

Abstract

We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents interact locally by their individual variables: for example, people working in the same office may influence their peers' expectations (optimism/pessimism are contagious), while people living in the same neighborhood may influence their peers' saving patterns (stinginess/largeness are contagious). Thus, for each type of variable there exists a different underlying social network, which we refer to as a ``layer''. Each layer connects the same set of agents by a different set of links defining a different topology. In different layers, the nature of the variables and their dynamics may be different (Ising, Heisenberg, matrix models, etc). The different variables belonging to the same agent interact (the level of optimism of an agent may influence its saving level), thus coupling the various layers. We present a simple instance of such a network, where a one-dimensional Ising chain (representing the interaction between the optimist-pessimist expectations) is coupled through a random site-to-site mapping to a one-dimensional generalized Blume-Capel chain (representing the dynamics of the agents' saving ratios). In the absence of coupling between the layers, the one-dimensional systems describing respectively the expectations and the saving ratios do not feature any ordered phase (herding). Yet, such a herding phase emerges in the coupled system, highlighting the non-trivial nature of the present framework.