For low values of the non-linear parameter buyers never build-up any fidelity. This is observed in figure 2 , which describes the dynamics obtained with = 0.8. The daily profit of buyers averaged over all buyers and over 100 days after a transition period of 100 days, is 0.0502. This result is lower than the average profit per transaction for the buyer . This is due to all those occasions on which a buyer visited an empty shop. The daily profit of sellers averaged over all sellers and over 100 days after a transition period of 100 days, is 0.6532. This result is lower than 10 times the average profit per transaction for the seller (the factor 10 corresponds to the average number of buyers per shop). This difference was also generated indirectly by buyers who visited empty shops since, at the same time, some shops with supplies were not visited, and this resulted in losses for their owner.
Figure 2: Charts for the disorganized regime (30 agents visiting 3 shops, when the learning parameter and ). a The organization process is monitored by simplex plots taken at times 10, 22 and 50. Even at time 50, agents are still scattered around the barycenter of the triangle, an indication of a disordered regime without preference of any agent for any of the shops. b Time plot of the order parameter y. c Performance log of morning transactions in shop number 1. The time charts display the initial quantity of goods to be sold every morning, the remaining unsold goods by the end of the morning, the number of customers, of those customers refusing the proposed price (which soon falls to zero for the present choice of a, b and ), and of those unsatisfied customers who did not manage to buy anything.
The order parameter, y fluctuates well below 0.50 and thus corresponds to randomly distributed . This feature is also clear from the simplex plots of the . Figure 2 shows that the performance of shop number 1 exhibits large fluctuations. The same is true for the two other shops.