A Market Share Theorem

Bell, D.E., Keeney, R.L., & Little, J.D.C. (1974). A Market Share Theorem. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-74-002

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Abstract

Many marketing models use variants of the relationship: Market share equals marketing effort divided by total marketing effort. Although the relation can be assumed directly, certain insight is gained by deriving it from more fundamental assumptions as follows. For a given customer group, each competitive seller has a real valued "attraction" with the properties: (1) attraction is non-negative, (2) two sellers with equal attraction have equal market share, (3) the market share for a given seller will be affected in the same manner if the attraction of any other seller is increased by a fixed amount.

A theorem proven states that if the relation between share and attraction satisfies the above assumptions, then share equals attraction divided by total attraction. Insofar as marketing factors can be assembled into an attraction function that satisfies the assumptions, the theorem provides a method for modelling market share.

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