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

and others for their valuable comments during the development and revision of this manuscript. 1 This paper is a substantial extension of the earlier paper, " Number and Competitors and Dynamic Stability of Competition: Five is a Crowd in the Market Share Attraction Model. " This paper replaces and extends the previous one. 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. Using simulation to conduct a non-equilibrium analysis of a market characterized by the market share attraction model shows that the relatively simple competitive behavior of optimizing one's own spending could lead to surprising instability. Optimizing one's own spending for the next period requires that firms either (1) use their competitors' last-period budgets and the MSA model to determine a profit-maximizing budget or (2) use current customer response (dollar marketing input-dollar profit output) to set profit-maximizing budgets. These two approaches are equivalent in that they produce identical spending decisions. These decisions are myopic in the sense that they are profit maximizing under current competitive conditions. The surprising finding is that this behavior leads to dynamic instability if the number of competitors exceeds a threshold level of four. Even though an equilibrium exists, myopic profit maximizing firms will not find it if the number of competitors exceeds four. In this paper, we provide an analytical explanation for the emergence of this instability and demonstrate the close relationship between this nonlinear system of competing firms and the standard logistic map. We go on to show that this threshold for instability persists even if one firm has perfect knowledge of future competitor actions. In this work, we also identify conditions that affect the existence and level of the instability threshold. 3 Not only in (biological) research, but also in the everyday world of politics and economics, we would all be better off if more people realized that simple nonlinear systems do not necessarily possess simple dynamical properties. May (1986)