In order to see whether there was any empirical evidence of ordered or disordered behavior of buyers in a market, we started from a data base of the 237162 transactions that took place on the wholesale fish market in Marseille from 1/2/1988 to 6/29/1991 inclusive. On this market over 700 buyers meet over 40 sellers, to trade different types of fish. The market is organised as in our model, that is, no prices are posted, sellers start with a stock of fish which has to be disposed of rapidly because of its perishable nature. Buyers are either retailers or restaurant owners. Deals are made on a bilateral basis and the market closes at a fixed time. Of course the model is a caricature of the real situation since the alternative for a buyer to purchasing his optimal good is, in fact, to purchase , in his view, some inferior alternative.
The direct examination of the 16 Mb transactions file with the help of standard sorting facilities reveals a lot of organisation in terms of prices and buyers preferences for sellers. In particular, one immediately observes that most frequent buyers, those who visit the market more than once per week, with very few exceptions visit only one seller, while less frequent buyers would visit several sellers, which is consistent with our model. The transactions data will be sumarized in this section in terms that only address the organisation issue. But since they data were collected, Marseilles GREQAM research teams have devoted a lot of effort to classifying and interpreting the data, and especially to investigate the price dynamics which, for instance, show price dispersion, and smaller prices by the end of the selling session (see Kirman and Vignes (1991) and Hardle and Kirman (1995)).
A first step in comparing our theory with empirical data is to check whether individual buyers display ordered or disordered behaviour during those three years. Since the classical approach to agent behaviour predicts search for the best price, and hence what we call the searching behaviour implying visiting different shops, any manifestation of order would tend to support our theoretical prediction. If we find evidence of ordered behaviour for certain participants, a second step is then to relate the difference in the observed behaviours of these traders to some difference between their characteristics and those of other buyers.
For the first step, the existence of faithful buyers, we consider statistics of cod, whiting and sole transactions in 1989. About 23 sellers offer cod, but the quantities that they sell are very different: the three biggest sellers respectively offer 43, 14 and 12 perc. of the fish sold on the market. Since we were interested in fidelity issues we only processed the data concerning the transactions of those 178 buyers that were present for more than 8 months on the market. A striking fact is that 86 of these buyers made a yearly average of more than 95 perc. of their monthly purchase with one seller! In other word, we would say that nearly half of the buyers were very faithful.
In the case of whiting and sole, faithful behaviour was slightly less frequent. For whiting, where the fractions sold by the 3 biggest sellers were 27, 8 and 8 perc., 55 buyers out of 229 purchased more than 95 perc. of their monthly purchase with one seller, but still 124 sellers purchased above 80 percent with one seller. The corresponding figures for sole were respectively 15, 14 and 14 for the largest fractions, 91 out of 280 buyers purchased more than 95 perc. of their monthly purchase with one seller, and 154 sellers purchased more than 80 percent with one seller.
To look at the second step, let us recall that in its crudest version, the theory that we propose relates fidelity to parameters (discrimination rate) and (cumulated profit). , the discrimination parameter probably varies a lot for different buyers, but we have a priori no direct way to test it. On the other hand is strongly and positively related to monthly purchases of buyers, which is empirically measured for all buyers.
Figure 4 sumarises buyers fidelities in terms of relative frequency of visits to their favorite seller as a function of their monthly purchase of cod . On can observe that fidelities are high in general, that a number of buyers visit only one seller, and that a cubic fit shows that fidelity increases with monthly purchase. All three features are consistent with our theory, and in contradiction with a random search behavior for all buyers.
Figure 4: Each dot is an empirical evidence from Marseilles fishmarket representing a buyer fidelity to his favorite seller (relative frequency of visits), as a function of his monthly purchase of cod in tens of kilograms. Low purchases correspond to unfrequent buyers, who generally visit once a week, while large purchase are those of buyers who visit nearly everyday the market opens. The continuous line is a cubic fit which shows that fidelity increases with monthly purchase.