  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.
