We have examined a simple model of a market in order to see how the "order" that is observed on many markets for perishable goods develops. "Order" here means the establishment of stable trading relationships over the many periods in which the market opens.
In the simplest model, we have shown analytically that an ordered regime appears whenever the agents discrimination rate among shops divided by the number of shops is larger than the reciprocal of the discounted sum of their profit. In the organized regime, buyers have strong preferences for one shop over all others and the market is rather stable. On the other hand, in the disordered regime, agents do not show any preference and market performance exhibits large fluctuations. The transition between the ordered and disordered regimes is continuous but very abrupt (at least for the simplest one session model) in terms of the order parameter.
Since individual properties of buyers govern the ratio of their discrimination rate to the threshold rate , a bimodal distribution of buyers, some with an ordered behavior some not, is to be expected in real markets. A comparison with empirical data from Marseille fishmarket indeed shows the existence of a bimodal distribution of searchers and faithful buyers, and the positive correlation of the faithful behavior with the frequency of transactions.
When more realistic assumptions are introduced, such as fluctuations in prices, and later sessions with lower prices to clear the market, simulations show that the critical value of the transition parameter is increased and the transition becomes somewhat less abrupt. However both regimes can still be observed. The simple model is thus robust with respect to changes that can be made to improve realism: its main qualitative property, namely the existence of two regimes of dynamical behavior is maintained.
Thus what we have shown within the context of an admittedly very simple model is that the presence of "order" and "organisation" in a market is very dependent on, and very sensitive to, the way in which agents react to their previous experience. As has been seen "order" in our model is more efficient in Pareto terms than disorder and it is therefore of considerable economic interest to be able to identify under which conditions "order" emerges.
We thank Derek Smith for help with the Tk/Tcl interactive display of simulation results, Rob Deboer for the use of his GRIND software, Paul Pezanis for his help in the analysis of Marseille fishmarket data, Nick Vriend for helpful comments, and Olivier Chenevez, Bernard Derrida, Jean Pierre Nadal and Jean Vannimenus for helpful discussions and important suggestions. The Laboratoire de Physique Statistique is associated with CNRS (UA 1306) ,Ecole Normale Supérieure, and Universités Paris 6 et Paris 7. This work was started during a visit by GW and AK to the The SantaFe Institute which we thank for its hospitality.