Bertels and Boman attempt to illustrate some of the problems of agent-based social simulations in markets using appropriate mathematical tools.

The paper contains three main parts. The first part, “Knowing the equations,” discusses specific desired behavioral properties of models that can be deterministically induced by a mathematical structure. The example the authors use is that of a model that simulates the buying behavior of consumers in the Marseille fish market. The second part, “Knowing the parameter regime,” is an exploration of the parameter regime of a model, demonstrating that this construction can be problematic and very labor intensive. The authors discuss an equation modeling population growth in terms of birth and death rates. The third part, “Modeling time,” presents some methodological aspects of alignment efforts and the modeling of time.

The paper points out some of the potential pitfalls in agent-based social simulations that one should be aware of when creating an agent-based model. A mathematical structure can generate desired or undesired behavior; because a small structural part of the model can have a great impact on the overall behavior, studying and testing the model is of great importance.

The authors conclude that in view of the fact that even relatively simple models can have multiple, multiple-valued parameters, parametric studies may be a practical impossibility.