Macroscopic approximation methods for the analysis of adaptive networked agent-based models: The example of a two-sector investment model

TL;DR

This paper introduces a statistical aggregation method combining moment closure, pair approximation, and thermodynamic limits to analyze complex adaptive networked agent-based models, demonstrated on an investment model with heterogeneous agents.

Contribution

It develops a novel analytical approach to approximate macro-dynamics of heterogeneous agent models on adaptive networks, enabling bifurcation and stability analysis.

Findings

The approximation accurately matches numerical simulations across various parameters.

The method reveals multi-stability and bifurcation phenomena in the model.

Analytical tools help understand emergent behaviors in complex adaptive networks.

Abstract

In this paper, we propose a statistical aggregation method for agent-based models with heterogeneous agents that interact both locally on a complex adaptive network and globally on a market. The method combines three approaches from statistical physics: (a) moment closure, (b) pair approximation of adaptive network processes, and (c) thermodynamic limit of the resulting stochastic process. As an example of use, we develop a stochastic agent-based model with heterogeneous households that invest in either a fossil-fuel or renewables-based sector while allocating labor on a competitive market. Using the adaptive voter model, the model describes agents as social learners that interact on a dynamic network. We apply the approximation methods to derive a set of ordinary differential equations that approximate the macro-dynamics of the model. A comparison of the reduced analytical model with numerical simulations shows that the approximation fits well for a wide range of parameters. The proposed method makes it possible to use analytical tools to better understand the dynamical properties of models with heterogeneous agents on adaptive networks. We showcase this with a bifurcation analysis that identifies parameter ranges with multi-stabilities. The method can thus help to explain emergent phenomena from network interactions and make them mathematically traceable.