The danger model: application to a competitive market

The behavior of the firm in a competitive market based on the idea of the human system, i.e., using a danger activator and a defence system, is modelled. The proposed model uses three variables: market share ratio, danger index and the ratio of relative investment between the firm and the total investments including the competition. The danger activator, the defence and the market reaction functions, which explain how the danger index becomes activated, how the firm reacts to a danger signal, and the market reaction to the firm’s actions, respectively, are carefully constructed. This leads to a parametric dynamic system that governs the behavior of the competitive market. The following five classical behaviors of a firm result: monopoly, below aimed market share, aimed market share, above aimed market share and out of market. Formulas for a sensitivity analysis are derived to determine how and how much the equilibrium points of the dynamic system change when the parameters change. All the concepts are illustrated by graphs that show the equilibrium points and the trajectories of the system.