A Dynamic Duopoly Game with Content Providers’ Bounded Rationality

Abstract

<jats:p> 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. </jats:p>

Analyzing the Dynamic Data Sponsoring in the Case of Competing Internet Service Providers and Content Providers

“…Credibility of content c f of CP f is a linear function of the quality of service (QoS) q ss f and the quality content (QoC) q c f , which is written as follows [16,34,36,37]:…”

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

“…In a real insurance market, we can consider the control action as the regulation on the price adjustment speed, and we can also consider the control action as the learning ability or adaptability of the market [40]. e time-delayed feedback control method can be used to make the system from a chaotic state to stable state, which ensures that the insurance market develops in an orderly way.…”

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“…Model. D ij is the average demand of end-users who connect to the CP i through the ISP j which depends on content access price p c i , credibility c i , network access price p s j , QoS q s j , and cache access price p cc j (see [31][32][33]). e demand D ij depends also on prices p c − i , credibilities c − i , prices p s − j , prices p cc − j , and QoS set by the opponents.…”

“…θ i c 2 i is the cost to produce the credibility of content c i . e credibility of content c i of CP i is a function of the quality of service q ss i and quality content q c i , which can be expressed as [33,[35][36][37]…”