A Model of Market Shares I

Consider a market in which firms sell a product that is differentiated along one quantifiable dimension (for example, the amount of CO₂ in seltzer water). Let there be a large number of consumers, each with a clearly defined preference for the size of the quantifiable dimension. Call these preferences the varieties. Assume that a consumer who cannot find his or her favorite variety will choose the one with a size of the quantifiable dimension closest to that of his or her favorite. Let firms randomly select a variety (indicated above by the gray tick marks) and observe the resulting sizes of the market shares (indicated by the orange and blue line segments).