Nonlinear Dynamic Model of a Microeconomic System with Different Reciprocity and Expectations Types of Firms: Stability and Bifurcations

This paper analyzes the dynamic interaction between selfish and reciprocity firms in the market of homogeneous product. The decisions of both types of firms in respect of their output strategies are investigated under naive, adaptive and generalized expectations. The standard postulate for competitive firms’ model has been extended by the assumption that there is a share of reciprocity firms which, unlike selfish firms, maximize both private and social benefits as consumer surplus. It has been proved that the unique Nash equilibrium is stable for all affordable values of parameters in the model with adaptive expectations, and is unstable for the model with naive expectations at sufficiently large number of firms in the market. A special desktop application has been created for animation of model trajectory and demonstration of stable quantity trajectories and bifurcation diagrams of firms’ output. Naive expectations of two-thirds of firms result in a state of dynamic chaos in the market leading to degeneration of the existing competition model between the two types of firms. The crucial factor which ensures the stable equilibrium in the market and the ability to predict firms’ output is the adaptive approach which takes into account the adaptive expectations of firms planning their product quantity.