Modeling and Decision Support for the Firms’ Pricing Policy under a Chaotic Dynamic of Market Prices

The article presents the results of the study of nonlinear market prices dynamic, simulated using game theory model, maps and theory of bifurcation. Market pricing is presented as a two-dimensional map. Qualitative analyses of the firms’ pricing system properties using the fixed points, analysis of the trajectories near these fixed points were fulfilled Simulation of the market prices dynamic showed that the fixed point of the map coincides with the local Nash equilibrium, so the analysis of the stability of Nash equilibrium was done based on the maps’ fixed points sustainability analysis. Numerical simulation results were visualized, bifurcations of the fixed point were identified and transition from periodic to chaotic mode was demonstrated. Sustainability analysis was carried out with using Jacobian. The mechanism for the pricing decision support, allowing under a chaotic market dynamics to ensure maximum efficiency of the firms was proposed.