Economic theory has developed a typology of markets which depends upon the number of firms which are present. Much of the literature, however, is set in the context of a given market structure, with the consequences of the structure being explored. Considerably less attention is paid to the process by which any particular structure emerges. In this paper, we examine the process of how different types of market structure emerge in new product markets, and in particular on markets which are primarily web-based. A wide range of outcome is possible. But the uncertainty of outcome of the evolution of market shares in such markets is based, not on the various strategies of the firms. Instead, it is inherent in the behavioral rule of choice used by consumers. We examine the consequences, for the market structure which emerges, of a realistic behavioral rule for consumer choice in new product markets. The rule has been applied in a range of different empirical contexts. It is essentially based on the model of genetic drift pioneered by Sewall Wright in the inter-war period. We identify the parameter ranges in the model in which the Herfindahl-Hirschman Index is likely to fall within the ranges identified by the US Department of Justice: unconcentrated markets; moderately concentrated markets and highly concentrated markets.