تکامل ساختار بازار:یک مدل ACE از پراکندگی قیمت و وفاداری

We present an agent-based computational economics (ACE) model of the wholesale fish market in Marseille. Two of the stylized facts of that market are high loyalty of buyers to sellers, and persistent price dispersion, although it is every day the same population of sellers and buyers that meets in the same market hall. In our ACE model, sellers decide on quantities to supply, prices to ask, and how to treat loyal customers, while buyers decide which sellers to visit, and which prices to accept. Learning takes place through reinforcement. The model explains both stylized facts price dispersion and high loyalty. In a coevolutionary process, buyers learn to become loyal as sellers learn to offer higher utility to loyal buyers, while these sellers, in turn, learn to offer higher utility to loyal buyers as they happen to realize higher gross revenues from loyal buyers. The model also explains the effect of heterogeneity of the buyers. We analyze how this leads to subtle differences in the shopping patterns of the different types of buyers, and how this is related to the behavior of the sellers in the market.

We study the working of the wholesale fish market in Marseille (France), and in particular we focus on the following two stylized facts that characterize this market: a widespread high loyalty of buyers to sellers, and persistent price dispersion. Our real interest as economists is not in fish markets per se, and unlike the Scots we would not question the relevance of any story just heard with the standard expression ‘but what’s it got to do with the price of fish?’. But casual observations suggest that these stylized facts are common to many other markets, 1 we do believe that some of the insights developed in this study might be carried over to such markets. More in general, we believe that if we want to understand the dynamics of interactive market processes, and the emergent properties of the evolving market structures and outcomes, it might pay to analyze explicitly how agents interact with each other, how information spreads through the market, and how adjustments in disequilibrium take place. As we argued elsewhere (e.g., Kirman, 1994; Vriend 1994, Vriend 1995 and Vriend 1996, or Vriend, 1999), a natural way to do this is following an agent-based computational economics (ACE) approach. Two additional reasons why we were attracted to studying this specific market are, first, that we have a unique data set containing the records for all single transactions that have taken place in this fish market over a number of years. This is a very rich data set, but at the same time it has some severe limitations, as there are, for example, no data concerning market interactions that did not lead to transactions. Second, this wholesale fish market is a relatively simple, well-defined, and well-structured market (cf. the ‘market’ for second-hand cars). Moreover, fish is a perishable commodity, implying that the issue of the strategic use of inventories does not arise (cf. the early literature on market microstructures in finance; see, e.g., O'Hara, 1994). The paper is organized as follows. In Section 2, we will sketch the Marseille fish market, and discuss the two not easily explained stylized facts. In Section 3, we present an ACE model of the market. Section 4 analyzes the model, and Section 5 concludes.

Our ACE model of the Marseille fish market, focussing on an explicit consideration of the market interactions between the individual agents, explains both stylized facts price dispersion and loyalty as the outcome of a coevolutionary process, in which both sides adapt to their changing environment. Buyers learn to become loyal, as sellers learn to offer a higher payoff to loyal buyers, while these sellers, in turn, learn to offer a higher payoff to loyal buyers, as they happen to realize a higher payoff from loyal buyers. In some sense, the basic problem is one of coordination, and loyalty works as a coordination device. This suggests that developing loyalty has some similarity with sending intrinsically meaningless signals, say, like wearing a blue shirt. The similarity lies herein that there is nothing intrinsic in loyalty that makes it pay, as there are no real switching costs in our model (cf. Klemperer, 1995). Hence, at first sight one might conjecture that our explanation could as well have gone the other way around: ‘Buyers learn to become non-loyal, as sellers learn to offer a higher payoff to non-loyal buyers, while these sellers, in turn, learn to offer a higher payoff to non-loyal buyers, as they happen to realize a higher payoff from non-loyal buyers.’ However, although there is some similarity with intrinsically meaningless signals, there are also some important differences. Loyalty, whatever its degree, develops automatically as a result of market behavior, without explicit additional non-market decisions like the color of one's shirt. Moreover, being loyal or non-loyal has a direct economic meaning. Suppose, for example, that there appears to be some serial correlation in a seller's decisions, and that a buyer is satisfied with that seller. Loyalty would benefit that buyer, but continuing to dress blue while shopping around randomly would not. Or suppose that a seller offers a poor service. One of his buyers becoming non-loyal would hurt, but that buyer merely changing the color of his shirt would not. Loyalty means continuity, and allows buyers and sellers to avoid unproductive meetings. A variant of the model with multiple types of buyers explains how buyers who can resell outside the market for a higher price develop a pattern of shopping behavior characterized by higher loyalty such that they find higher prices in the market, and experience a better service. The sellers do not explicitly recognize different types of buyers (cf. Borenstein, 1991). But this price and service discrimination emerge as, in coevolution with the development of shopping patterns which differ in a subtle way among the buyers, the sellers on the one hand learn to recognize these differences implicitly, whereas on the other, different types of sellers emerge. Hence, the underlying incentive, that missing out on a transaction is more costly for those buyers with a higher resell price, does not only lead those buyers to accept more prices, but it also leads to differences in shopping patterns and to differences among the sellers in ways that seem consistent with real markets. To conclude, let us stress how simple our ACE model is, and which factors do not play a role in our model. We did not assume any real switching costs or search costs, and we show that to explain loyalty and price dispersion, there is no need to assume given social networks, direct personal relations, or cultural factors (cf. Richardson, 1960). In fact, in our model all sellers and all buyers are identical ex ante. In a variant of our base model, there are three types of buyers, but even there, our ACE model explains that for price and service discrimination to occur (plus the related loyalty), it is not necessary that the sellers explicitly recognize these different types of buyers. All agents in our model have very limited cognitive capabilities, and they cannot engage in sophisticated reasoning processes. The buyers do not even know what the concept of loyalty means, and sellers only recognize how familiar faces look to them, but do not recognize the identities of individual buyers as such. As the agents are not looking forward (and reasoning backward) beyond the end of the day, they do not play dynamic strategies. Each agent simply learns through reinforcement only. Hence, our ACE model of price dispersion and loyalty highlights the role of the evolving incentive structure of the market.27