The Distribution of Market Shares in Monopolistically Competitive Markets
Existing models of the distribution of market shares are based on the idea of preferential attachment. A mechanism is postulated that causes firms with relatively larger market shares to be more likely to attract additional customers. Over time, this process of proportional growth gives rise to the observed right-skewed distribution. Similar models have been used to explain the distribution of city sizes, firm sizes, and links to nodes in various social networks. Implicit in all these models is the assumption that without the mechanism of preferential attachment, the distribution would be symmetric.
In this paper, a model is presented that shows that a right-skewed distribution of market shares can arise from randomness, without any assumption of preferential attachment, or proportional growth. A computational model is constructed in which firms randomly differentiate a product that is sold to a population of consumers with uniformly distributed preferences. Computer simulations of industries with varying numbers of competitors show the resulting distributions of market shares to be right-skewed, and to closely match actual distributions.