Why is Five a Crowd in the Market Share Attraction Model: The Dynamic Stability of Competition

28 Pages Posted: 6 Sep 2001  

Paul Farris

University of Virginia - Darden School of Business

Phillip E. Pfeifer

University of Virginia - Darden School of Business

David Reibstein

Marketing Science Institute; University of Pennsylvania - Marketing Department

Erjen van Nierop

Carnegie Mellon University - David A. Tepper School of Business; Erasmus Research Institute of Management (ERIM); Tinbergen Institute

Date Written: August 2001

Abstract

As economists have increasingly accepted the notion that non-equilibrium behavior may be a reflection of the real world, interest has grown in modeling the emergence of turbulence as well as equilibrium. Earlier work by two of the authors used simulation to conduct a non-equilibrium analysis of a market where customer reaction followed the market share attraction model. These simulations demonstrated that even the relatively simple competitive behavior of optimizing one's own spending levels could lead to surprising instability. Optimizing one's own spending requires either that firms use their competitors' last-period budgets and the MSA model to determine a profit-maximizing budget for the next period or that firms use current dollar marketing-dollar profit response to set budgets for next period. Application of either logic will lead to dynamic instability when the number of competitors exceeds a threshold level of four. This study provides an analytical explanation for the emergence of this instability and demonstrates the relationship between this system of competing firms and the standard logistic map. This work also extends the original model formulation to identify conditions that affect the existence or level of the instability thresholds.

Suggested Citation

Farris, Paul and Pfeifer, Phillip E. and Reibstein, David and van Nierop, Erjen, Why is Five a Crowd in the Market Share Attraction Model: The Dynamic Stability of Competition (August 2001). Darden Business School Working Paper No. 01-21. Available at SSRN: https://ssrn.com/abstract=282535 or http://dx.doi.org/10.2139/ssrn.282535

Paul Farris (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States
434-924-0524 (Phone)

HOME PAGE: http://www.darden.virginia.edu/faculty/farris.htm

Phillip E. Pfeifer

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States
434-924-4803 (Phone)

HOME PAGE: http://www.darden.virginia.edu/faculty/Pfeifer.htm

David Reibstein

Marketing Science Institute ( email )

1000 Massachusetts Ave.
Cambridge, MA 02138-5396
United States

University of Pennsylvania - Marketing Department

700 Jon M. Huntsman Hall
3730 Walnut Street
Philadelphia, PA 19104-6340
United States

Erjen Van Nierop

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Tinbergen Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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