Number of Competitors and Dynamic Stability of Competition: Five is a Crowd in the Market Share Attraction Model
22 Pages Posted: 16 Mar 2001
Date Written: January 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. It is well established that competitive actions and the associated reactions can destabilize a previously stable market. Earlier work by two of the authors used simulation to conduct a non-equilibrium competitive analysis of a market where consumer reaction followed the market share attraction model. These simulations demonstrated that even the relatively simple competitive behavior of optimizing ones own spending levels while assuming stable competitive behavior can lead to surprising instability. The basic logic of the market share attraction model is easy to accept. Given the amount of work done to fine-tune applications of this model, we believe the logic of the model helps determine the behavior of real firms. As shown in earlier work, however, application of the logic may lead to dynamic instability when the number of competitors exceeds a threshold level of three or four. This study provides an analytical explanation for the emergence of this instability when the number of competitors exceeds three or four. This work will also extend the original model formulation to identify other conditions that may affect the existence or level of the instability thresholds.
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