[Swarm-Modelling] foundation of ABMs

[Pablo Gomez Mourelo]

Dear all:

I am an engineer very  interested in agent-based modelling. I have a 
question for you all, related to justification/foundation of ABMs.
I have already read some literature and it seems to me that a 
justification of agent-based modelling has not been achieved (Volker 
Grimm).
One of the problems of AB-modelling is that randomness is nearly always 
included in our simulations, so different executions turn into different 
outcomes.
In comparison to mathematical models , it seems to me very difficult to 
develop a general theory (foundation) of agent based modelling. HOw do 
we know an ABM converges to some solution? How can we describe stability 
of an ABM?  Many modellers feel satisfied with the graphical output, but 
mathematicians always complain about the lack or rigour beneath the 
simulation.


My main question is: does anyone know of any paper/book giving a 
mathematical foundation of ABMs?

All the best,

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Pablo Gómez Mourelo
Departamento de Matemática Aplicada
ETSI Industriales
C/ Jose Gutierrez Abascal, 2
28006 MADRID
SPAIN
Universidad Politécnica de Madrid
Phone: +34 91 336 3105
Fax:   +34 91 336 3001
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