Which mathematical tools/approaches would be useful, or have been found to be useful, in modelling a 'manual agricultural' market economy amongst a closed group of ten to fifty households totalling up to 500 individuals in which a range of tools, crops and infrastructural facilities might be produced, maintained and exchanged across any desired number of periods and in which arbitrary individual propensities for each behaviour type of each individual can be expressed as temporal vectors, as can externalities such as climate, soil fertility, erosion and arrivals of itinerant sellers of externally produced trade goods?
My background suggests to me that Tensor Calculus is the point at which one should start looking for the means with which to achieve this. I suspect that the application of such tools to modelling the 'fluid' economic behaviour of social groups is not at an advanced stage of development. Has anybody any information or suggestions? Are 'game avatars' likely to be a fruitful source of useful algorithms? Thank you for any assistance or guidance...