In standard economic theory, the mechanisms which balance aggregate buyers' demand and sellers' supply and which organise the exchanges necessary to clear the market are left unspecified (Adam Smith's "invisible hand"), or assume some fictitious central organism (Walrasian tatonnement). The main idea behind this simplification is that supply and demand adjust during a preliminary phase until equibrium prices are reached. Transactions that clear the market are then performed in some unexplained way.
Standard "search models", (see, for example Diamond (1989)), have been developped to deal with situations in which different prices may be charged by individual sellers for the same good. In these, buyers sample sellers according to some rule and buy from the cheapest. All sellers are anonymous and are searched with equal probability. Such models seem to be plausible for transactions which take place infrequently and where the gain in information obtained by searching makes such searching worthwhile. This is the case, for example, when an individual purchases a car or a firm purchases an expensive piece of equipment.
Yet many other markets are ones on which individuals trade frequently for relatively inexpensive goods. On such markets it seems to make intuitive sense to profit from the experience gained from previous transactions to select a supplier and this may lead to the establishment of preferential links between buyers and sellers. Of particular interest is the case of markets for perishable goods. Since sellers cannot hold inventories, accurate prediction of the number of customers and of their demand is important. The more loyal the customers the better the prediction and the more likely the customer is to find the goods he is seeking. Thus the establishment of regular trading relationships may be mutually profitable. The basic aim of this paper is to examine the extent to which agents in a simple model of such markets will learn their way to establishing trading links. Our interest is thus to develop a model which is more adequate for transactions that are made often and on a repeated basis than standard search models.
The present model is related to adaptive economic models, in which agents are not endowed with perfect rationality, but behave according to some procedural rationality, using information obtained from other agents or from their own experience. A typical example of such an attitude is imitation, which may be motivated by the success of the other agents or by inference about the information they possess. A number of authors have adopted this approach, in particular those who use discrete choice theory, (see e.g. Aoki (1996), Brock and Durlauf(1995), Durlauf(1990), Kirman(1993), Lesourne(1992) and Anderson et al (1992) for a recent review of the discrete choice theory literature).
However, when transactions are not made public, agents have to rely on other sources of information. In particular, in many markets such as the Marseille fishmarket, from which our empirical evidence is drawn, prices are not posted and agents have to rely on their own experience. Hence, any model which seeks to explain some of the phenomena that characterise that type of market must be based on learning from past experience.
Here we adopt an approach which allows us to obtain analytical results for the simplest version of our model and we then use simulations to check that these results still hold in more complicated versions.
The structure of the paper is as follows. We start by proposing a very simple model of a market for a perishable good, in which buyers,(retailers), meet sellers,(wholesalers) and buy quantities of the homogeneous good to resell on their own local market . At each time step, buyers can purchase one unit of the good in a shop which is chosen according to the information gathered from previous purchases. This model is analytically solved using the "mean field" approximation. The theory predicts that two distinct types of behaviour for the agents should be observed according to their learning and choice parameters: some agents should remain faithful to one selected shop, while other should keep on shopping around for ever. We then use multi-agent simulations to study more complex, and more realistic versions of the model. These involve, for instance, several sessions of search and purchase during the same day, varying prices, and some more adaptive behaviour of buyers and sellers. Our simulations show that the same patterns of dynamical behaviour persist. We finally verify that our theoretical predictions are consistent with the empirical data from the wholesale fishmarket in Marseille.