Why is Five a Crowd in the Market Share Attraction Model: The Dynamic Stability of Competition
28 Pages Posted: 6 Sep 2001
Date Written: August 2001
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.
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