A Dynamic Investigation into Logically Consistent Market Share Models

This paper introduces a dynamic zero-sum game framework inspired by the Lanchester combat model to resolve issues that relate to logically consistent market share models. Our new theorem. shows that three of four axioms in Bell, Keeney and Little's (1975) "market share theorem" are either incomplete or unnecessary; concerns about the nonlinearity and asymmetry aftermath of the market share system also are incorporated into in our analysis. Implications of this new theorem resolve some of the confusion surrounding the logically consistent market share models proposed by Naert and Bultez (1973) and McGuire and Weiss (1976), and the recent empirical paper by Brodie and de Kluyver (1987). More specifically, this pap;er explains the ways to incorporate both range and sum constraints to complete the logical consistency problem, and demonstrates the feasibility of adopting model robustness and descriptive validity which previously have been thought to be incompatible in construction of market share response models.

Issue Date:
Aug 01 1989
Publication Type:
Working or Discussion Paper
Record Identifier:
Total Pages:

 Record created 2017-07-12, last modified 2018-01-23

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