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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