Equation-based versus agent-based modeling

Basically, two modeling paradigms can be discerned:


builds on an interrelation of a set of equations that captures the variability of a system over time (ordinary differential equations - ODEs) or over time and space (partial differential equations - PDEs) An example would provide the development of pressure in a box. EBM does not aim at representing the micro-level behavior of individual agents in the first place (e.g. the velocity of individual gas particles in the box). Therefore, EBM tends to focus the modeler’s attention on the overall behavior of the system. Its basic constituencies are levels and flow rates, and not so much individual components.

Usually, EBM is primarily validated on the systems level by comparing model output with real system behavior. Since behavior of individual components is not explicitly in its focus, it usually is not validated on this level.

Furthermore, EBM (when restricted to ODE-methods like System Dynamics) has no intrinsic option for representing space (PDEs provide parsimonious options for modeling physical space, but not the interaction space of individual agents).

Several intuitive drag-and-drop tools for constructing and analyzing system dynamics models exist (Stella, Powersim, Simulink (of Matlab) or VENSIM) which makes EBM relatively easy to use and therefore attractive and widely applied. At times however, for the same reason it is often deployed in cases where its appropriateness could be questioned.

In sum, EBM seems well-suited to represent physical processes (or processes that can be seen as such without loss). It suggests regarding a system as a whole in the first place and does not support an explicit representation of components (agents). To some extent hence, EBM has to be regarded as top-down technology. It is most naturally applied to systems that can be modeled centrally, and in which the dynamics are dominated by physical laws rather than by information processing.


usually starts out with modeling properties and behavior of individual agents and only thereafter considers macro-level effects to emerge from the aggregation of agents’ behavior. In ABM, the individual agent is the explicit subject to the modeling effort. The system – e.g. swarm behavior – is expected to emerge from the interaction of individual agents.

With this, ABM offers an additional level of validation. Like EBM it allows to compare model output with observed system behavior. Additionally however, it can be validated at the individual level by comparing the encoded behavior of each agent with the actual behavior of real agents. This however, usually requires additional data and hence more efforts in empirical research.

Basically, ABM might seem intuitively more appropriate for modeling social systems, since it allows, and even necessitates, considering individual decisions, dispositions and inclinations. Its natural modularization follows boundaries among individuals, whereas in EBM modularization often crosses these boundaries.

What is more, ABM allows representing space, thereby offering possibilities to consider topological particularities of interaction and information transfer. In combination with graph theory and network analysis it enables precise conceptualizations of differences in frequency, strength, existence etc. of interactions between agents.

Disadvantageous might seem that ABM so far inevitably necessitates coding skills. Although, some modeling platforms (Repast, Anylogic) try to offer drag-and-drop options for coding, and others (like Netlogo) try to minimize programming efforts by using relatively intuitive programming languages, at the time being ABM definitely requires more technical knowledge and efforts than EBM.

In sum, ABM seems most appropriate in domains characterized by a high degree of localization and distribution and dominated by discrete decisions. Its approach is bottom-up, it allows to consider spatial particularities of a system, but it requires more technical knowledge and it also needs more elaborate empirical research.

Several examples exist where the two approaches have been fruitfully combined (see Fishwick 1995, Wilson 1998).

Bibliography (selection)