A theoretical formalism for analyzing agent-based models

Purpose: Following Holland, complex adaptive systems (CASs) are collections of interacting, autonomous, learning decision makers embedded in an interactive environment. Modeling CASs is challenging for a variety of reasons including the presence of heterogeneity, spatial relationships, nonlinearity, and, of course, adaptation. The challenges of modeling CASs can largely be overcome by using the individual-level focus of agent-based modeling. Agent-based modeling has been used successfully to model CASs in many disciplines. Many of these models were implemented using agent-based modeling software such as Swarm, Repast 3, Repast Simphony, Repast for High-Performance Computing, MASON, NetLogo, or StarLogo. All of these options use modular imperative architectures with factored agents, spaces, a scheduler, logs, and an interface. Many custom agent-based models also use this kind of architecture. This paper's contribution is to introduce and apply a theoretical formalism for analyzing modular imperative agent-based models of CASs. This paper includes an analysis of three example models to show how the formalism is useful for predicting the execution time and space requirements for representations of common CASs. Method: The paper details the formalism and then uses it to prove several new findings about modular imperative agent-based models. Results: It is proven that the asymptotic time and space performance ofmodular imperative agent-based modeling studies is computationally optimal for a common class of problems. Here 'optimal' means that no other technique can solve the same problem computationally using less asymptotic time or space. Modular imperative agent-based models are shown to be universal models, subject to the correctness of the Church-Turing thesis. Several other results are also proven about the time and space performance of modular imperative agent-based models. The formalism is then used to predict the performance of three models and the results are found to compare closely to the measured performance. Conclusions: This paper's contribution is to introduce, analyze, and apply a theoretical formalism for proving findings about agent-based models with modular agent scheduler architectures. Given that this kind of modeling is both computationally optimal and a natural structural match for many modeling problems, it follows that it is the best modeling method for such problems.