The idea of a market with a uniform price is not realistic and we wanted to check the influence of price variations on the agents' behavior. In fact, the above section 3.2 on hysteresis already gives us a clue as to the possible results of price changes: price differences resulting in profit differences for the buyer lower than the width of the hysteresis curve do not change fidelity and then should not distroy order. Figure 1 shows that this width in profits is around 20 perc.(and hence 40 perc. in prices) when is 25 perc. above the theshold for order.
We made simulations with morning price fluctuating in each shop with an auto-regressive trend towards the morning price computed to maximize profits p. Price is also decreased when potential buyers refuse the offer, a situation seldom encountered by the end of the simulations as mentioned earlier. The morning price of each shop is then varied in the simulations according to the following expression:
is a stochastic multiplier with average 1, n and are respectively the number of customers of the shop and the number of customers having refused the previous price during the last session.
The simulation results are remarkably close to the results obtained with constant morning price for both sessions: the transition is sharpened and order is obtained for slightly lower values of .