Interaction and Market Structure

This volume contains a set of papers which pursue the aim of examining how the properties of aggregate economic variables are influenced by the actions and interactions of individuals. This has been the central theme of a series of workshops held at the University of Ancona, Italy, since 1996, whose general title is Workshops on Economics with Heterogeneous Interactive Agents (WEHIA for short).¹

In this paper we study the behavior of boundedly rational agents in a two good economy where trading is costly with respect to time. All individuals have a fixed time budget and may spend time for the production of good one, the production of good two and trading. They update their strategies, which determine their time allocation, according to a simple imitation type learning rule with noise. In a setup with two different type of agents with different production technologies we show by the means of simulations that both direct trade and trade via mediators who specialize in trading can emerge. We can also observe the transition from a pure production economy via direct trade to an economy with mediated trade.

We study 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 the same population of sellers and buyers meets in the same market hall on every day. We build a minimal model of adaptive agents. Sellers decide on quantities to supply, prices to ask, and how to treat loyal customers. Buyers decide which seller to visit, and which prices to accept. Learning takes place through reinforcement. We analyze the emergence of 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 tum, learn to offer higher utility to loyal buyers as they happen to realize higher gross revenues from loyal buyers.

In this paper we study a class of dynamic promotional competition models, in which firms compete for market share by expending marketing effort. We investigate two main issues. First, we answer the question if it is possible to give a global characterization of the stability of the steady state effort allocation. We show that by using the concept of critical curves and an invariance property of the coordinate axes a characterization of the set of feasible points (points that generate positive trajectories converging to the steady state allocation) and its changes can be given. Second, we deal with the assumption of homogeneous firms, which is often made in the literature. We demonstrate that the symmetric model which derives from this assumption exhibits, in many situations, non-generic dynamical behavior. New phenomena, like Milnor attractors and synchronization of trajectories, arising in the homogeneous case are illustrated. The introduction of small heterogeneities into the model invalidates many of the conclusions derived under the hypothesis of homogeneous firms.

The paper takes up a Schumpeterian prototype model by K. Iwai (JEBO 1984) on the interplay of technological innovation and diffusion. In a first part, the deterministic version of the model is considered and its long-run equilibrium notion of a wave train is related to Iwai‘s analysis. The subsequent simulations of the full version of the model with a stochastic arrival of innovations typically yield long oscillations in the growth rates of average productivity. These long waves can be viewed as originating with the frequency distribution of techniques on a wave train, from which the economy is disturbed and back to which it continuously seeks to adapt, where it is in the very nature of this adjustment process to take several decades. Across a wide range of parameter scenarios, the average wave lengths are found to be closely related to the lifetime of techniques in the underlying deterministic economy. Furthermore, the lags between innovation activities and productivity growth are examined.

We study the implications of agents’ heterogeneity for business cycle analysis with the help of a two dimensional non-linear dynamical system derived from a New Keynesian macroeconomic model with imperfect capital markets. In order to analyze the interaction between real and financial variables, we have focussed on the degree of financial fragility of the economy, as proxied by the ratio of corporate net worth to the stock of capital, that is the equity ratio. Our approach allows to analyze both fluctuations due to the impulse-propagation mechanism and self-sustaining endogenous cycles. In the former case, shocks transmitted and amplified by a propagation mechanism, which depends on the degree of agents’ heterogeneity. In the latter case self sustained business cycles are generated by the evolution over time of the distribution of heterogeneous agents, classified by the degree of financial fragility.

In a basic model of monetary dynamics we allow inflationary expectations to be formed as a weighted average of fundamentalist and chartists expectations. The fundamentalists form inflationary expectations rationally in the traditional sense in that they have full knowledge of the economic environment. The chartists form expectations by using standard trend chasing expectations schemes. As inflation acceleratesfdeccelerates an increasing proportion of agents switch from chartism to fundamentalism and fundamentalists put increasing weight on a reversion towards the fundamental value. The study the dynamics of the resulting economic system and show that it can exhibit a range of complex dynamic behaviour.

This paper proposes an extension of the inventory production model developed in Bak, Chen, Scheinkman, and Woodford (BCSW, 1993). We show how the Pareto-Levy type of aggregate distributions emerge in global models as well as in local models. We extend the BCSW model by allowing random connections between firms. The distribution of production in the economy follows a power law probability distribution. In addition, the long-run frequency distribution follows the same law.

The work analyses the properties of international technological diffusion with interdependent markets in presence of some form of dynamic increasing returns and externalities, heterogenous agents and stochastic adoptions. We build and refine upon previous results from Bassanini and Dosi (1998), where a) we show the conditions of convergence to either technological monopoly or market sharing ultimately depending on the balance between increasing returns and degrees of agents’ heterogeneity, and b) we establish the (different) rates of convergence to either limit states. In the multi-market, international, extension considered here we determine the conditions yielding to world monopoly or conversely to world market sharing cum local monopolies. Together, the model accounts also for the rare empirical occurence of stable market sharing in each single market on the grounds of the (slower) rates of convergence that such a limit configuration entails.

I apply three noncooperative models of coalition formation to a Cournot olygopoly. In each model, each firm has to choose the coalition it wants to belong to. But each of this models is characterised by a different assumption that defines what happens to a coalition from which one or more players depart (which we shall refer to as a “depleted coalition”). In the first model proposed by Von Neumann and Morgenstern [1944], this depleted coalition is assumed to “fall apart”, in the second one proposed by Hart and Kurz [1983], it is assumed to “stick together”. I prove that the results depend crucially on the game of coalition formation. In the first model, the grand coalition is stable, in the second model, the unique stable structure is the structure in which all the firms are independent. In fact, The assumption that characterises the game of coalition formation has to be considered as a threat, the credibility of which has to be analysed. That is why I propose a third game in which members of a depleted coalition choose the reaction to adopt. It turns out that the members of such a coalition stick together as long as they are sufficiently numerous. As a result, the set of stable structures in this model depends on the number of firms, n. When this number is small, the grand coalition is the unique stable structure. But when the number of firms increases, asymmetrical coalition structures appear. For great value of n, stable structures appear with several coalitions, that can be of different sizes. We notice that, in this game with symmetric firms as players, the result can be asymmetric.

One of the main problems with the notion of correlated equilibrium is the lack of an explicit rationale for the correlation mechanism that is adopted. This paper investigates the conditions under which a specific correlation mechanism may be selected through a social learning process in a population of boundedly rational players that are randomly matched to play a coordination game. The selection process among correlation mechanisms is defined by replicator equations and the qualitative features of the dynamics are analyzed for the general case with n correlation devices. It is found that the dynamics generically select one specific mechanism among the alternative ones, thus bringing about a social standard of choice, i.e. a conventional way of correlating players‘ actions in anonymous interactions. This result then provides a strong evolutionary rationale for correlated equilibrium as a solution concept for coordination games.

In this paper we build a spatial, aspiration-based model of learning in the context of a quantity setting oligopoly from which we want to explore the conditions that lead to the emergence of cooperation among firms. We consider an economy consisting of many identical duopoliesj each duopoly is placed on a square of a torus. The duopolists are boundedly rational agents which adopt a very simple behavioural rule: if they are earning at least average profits, they do not change their strategies; if they are earning below-average profits they imitate the strategy adopted by one of their neighbours. We consider many variations to this general setting and, in most of the cases, we get results that support cooperation among firms.

In economics expectations play an important role. In making decisions agents form expectations about future values of variables. Therefore, in any dynamic economic model, agents beliefs about the future have to be modeled. Do people form expectations using a simple rule of thumb or do they use a continually updated forecasting rule? Can people learn a rational expectations equilibrium? This paper describes experiments where we investigate how people form expectations in the simplest dynamic economic model, the cobweb model, without any knowledge of the underlying market equilibrium equations. We found that only about 35% of the subjects seemed to be able to learn the unique rational expectations equilibrium. We also found that many individuals deviate from rational expectations for long periods of time, sometimes with ‘systematic forecasting errors’.

Our objective in this paper is to try and clarify what we perceive to be two major approaches to the problem of heterogeneous interactive economic agents, and argue in favor of the option which we feel has suffered relative neglect. The first option, perhaps best represented by the work of Alan Kirman, but found throughout the avant garde of the profession, tends to characterize agents as flawed automata or limited computational entities. Exercises in this tradition tend to produce simulations of specific economic situations. While there is much to admire in this program, we maintain that invoking a gestalt reversal which regards markets as computational devices, or literal formal automata, would achieve many of the same goals as the former research program, but would foster a rich and viable evolutionary economics to boot, one which would encourage both mathematical rigor and historical relevance, while avoiding many of the mechanistic excesses of neoclassical theory. Because the second path is the road less traveled, we survey what we call a computational understanding of markets, in order to provide a framework for incorporation of automata theory into a consciously evolutionary approach. For after all, what is the purpose of acknowledging the heterogeneity of agents, if not to then subject them to some form of selection process? We work through an explicit example ofthe automata theory approach, using two papers by Gode & Sunder [1993, 1997] to illustrate how some recent literatures could be recast into this novel approach. We close with the suggestion that it is experience with real-time markets being run as automata on computers, and not just some academic simulations, which will induce both economists and market participants to come to an appreciation of this kind of evolutionary economics.