We will discuss, in this section, further refinements of the simple model and see what influence they have on the behaviour of the agents. All the variants to be discussed share the same fundamental mechanism by which buyers choose sellers and the same way of updating preference coefficients as defined in section 2.2.The difference comes from the fact that sellers may choose the prices and quantities taking into account the fact that they can make further transactions.
These more realistic variants of the model are no longer analytically tractable and we are therefore obliged to resort to computer simulations to compare their dynamical properties with those of the simple soluble model and with empirical data.
It is important at this stage to specify the type of comparison that we intend to make between the variants of the model and empirical evidence. We certainly expect some changes to occur at the global level when modifications are introduced in the way in which individual agents make their decisions. Nevertheless, the main point here is to check whether the generic properties of the dynamics are still preserved after these changes. The existence of two distinct, ordered and disordered regimes, separated by a transition, is for instance such a generic property. On the other hand, we consider as non-generic the values of the parameters at the transition and the values of variables in the ordered or disordered regime. Since even the more elaborate versions of our model are so simplified in comparison with a very complex reality, a direct numerical fit of our model with empirical data would not be very satisfactory. This is because so many parameters which are not directly observable are involved. But the search for genericity is based on the conjecture that the large set of models which share the same generic properties also includes the real system itself. This conjecture, which is basic in the dynamical modeling of complex systems, rests on the notion of classes of universality in physics or of structural stability in mathematics.