Nonlinear dynamics and adjunct profits in two boundedly rational models of monopoly

Abstract

This paper studies the dynamic characteristics of a nonlinear monopoly model involving two boundedly rational monopolists with different information and knowledge on the market demand. The ℓ-monopolist knows only the actual values of output and the profit in the immediate past two periods, whereas the k-monopolist knows the marginal revenue but lacks computational ability to solve the profit maximization conditions. The price and cost functions are assumed to be cubic. These monopolists adopt a gradient-based method to determine their productions. For the dynamics of the ℓ -monopolist, the stability conditions and the explicit forms of the period-4 periodic points are obtained. The k-monopolist loses stability through a supercritical Neimark–Sacker bifurcation and a period-doubling bifurcation when the expected demand is formed with the past data. For comparison of the economic gains of the monopolists, the average profit associated with the nonlinear dynamics are calculated. It is numerically demonstrated that more information does not necessarily mean more profit.