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A Model of Market Structure Dynamics with Boundedly Rational Agents

Tatsuo Yanagita 1Tamotsu Onozaki 2

1. Hokkaido University, Research Institute for Electronic Science, Sapporo 060-0812, Japan
2. Aomori Public College, Faculty of Management and Economics, Aomori 030-0196, Japan

Abstract
A market economy is a typical complex adaptive system which consists of a large number of adaptive agents involved in parallel local interactions. These micro-level local interactions give rise to a certain macro-level spontaneous order, and then, the macro-order plays the role of binding conditions for micro-behavior. Complex dynamical behavior emerges as a consequence of recurrent causal chains among individual behavior and the macro-order.

In the present paper, we formulate a goods market as a complex adaptive system consisting of locally interacting, boundedly rational agents, i.e., firms and consumers. We posit market share distribution as the macro-order of a market economy, and a special attention is paid on the market share dynamics. At each time period, consumer has a given amount of income and determines from which firm to purchase goods, and then spends all his income so as to purchase as much as he can do. We employ the statistical description of consumer's behavior: The Bolzmann distribution is used to represent firm's share distribution of consumer, which is characterized by “temperature” in physical systems describing how greedily consumer pursues higher utility. Such consumer’s greediness is one of the important parameters controlling consumer’s behavior. On the other hand, firm does not know the shape of demand function it faces, so that it revises production and price so as to raise its profit with the aid of reinforcement learning algorithm, i.e., by learning through its experiences. We mainly focus on the dynamical phases which emerge as consumer’s greediness changes.

Numerical simulations show that, depending on consumer’s greediness, there appears three typical phases, i.e., statrionary equi-share coexistence phase, market-share battle oligopoly phase, and changing monopoly phase. It is also shown that, in an oligopolistic and monopolistic phases, the distribution of market share exhibits a long-tail and it follows Zipf’s law. It is also shown that the size of a firm and its growth rate are independent in the same situation (Gibrat’s law). Furthermore, it is shown that there is an optimal greediness at which each consumer maximizes his time-averaged utility.

 

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Presentation: Oral at International Conference on Economic Science with Heterogeneous Interacting Agents 2008, by Tamotsu Onozaki
See On-line Journal of International Conference on Economic Science with Heterogeneous Interacting Agents 2008

Submitted: 2008-03-24 22:19
Revised:   2009-06-07 00:48