Analysis of the Chaotic Dynamics Duopoly Game of ISPs Bounded Rational

Abstract

We propose in this paper an investigation of the dynamical behaviors of a duopoly model with two Internet services providers (ISPs). The competition between them is assumed to take place in terms of their pricing decisions and their number of cached items. According to the ISPs’ rationality level, we consider a scenario where both ISPs are bounded rational. Each ISP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamic system induced by bounded rationality and establish a necessary and sufficient condition for the 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.

5 G and beyond wireless network optimization through RIS technology: a pricing game

“…Therefore, the RISHs in the game gradually adjust their strategies based on existing data on the distribution of network costs and demand. That is, each RISH (say, the ith one) modifies its shared frequency band (q i (t)) depending on his profit margin [12][13][14] defined by: ∂u i (q i (t), q e j (t + 1))…”

“…The authors in [12] proposed a duopoly game model that interprets the dynamic behaviors in the telecommunications service provider environment. In addition, bounded rationality has been used for pricing management of resources in internet service providers' games, providing individual optimal solutions [13,14]. As connectivity demands continue to increase [15], Wireless Service Providers (WSPs) may face costly problems.…”