A Dynamic Duopoly Game with Content Providers’ Bounded Rationality

Abstract

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs’ rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control.