Dynamics of a market with heterogeneous learning agents

Abstract

We study a simple market model of heterogeneous interacting agents. There are two types of agents, consumers and firms, who are boundedly rational in the sense that they only have partial information. The consumers have a given amount of income at each time period. They determine from which firm to purchase goods, and then spend all the income to purchase as much as they can. The amount of goods they can obtain depends not only on the price offered by the firm but also the amount produced by the firm and the number of customers of the firm. We employ a statistical description of consumers’ behavior. The Bolzmann distribution is used to represent firms’ share distribution of consumers, which is characterized by a parameter (called “temperature” in physical systems) describing how greedily the consumers pursue higher utility. The firm does not know the shape of demand function it faces, so it revises production and price so as to raise its profit with the aid of a simple reinforcement learning rule which is applied to the “one-armed bandit” problem. Numerical simulations show that there is an optimal greediness, which maximize the time average of consumers’ utility. In the vicinity of the optimal greediness, oligopoly emerges although its membership changes frequently. In an oligopolistic market, the market share distribution of firms follows Zipf’s law.