New insights from a bounded rationality analysis for strategic price-QoS war

We present a game theoretic framework for the dynamical behaviors of a duopoly game in telecommunications service providers´ context. Competition between two Service Providers (SPs) is assumed to take place in terms of their pricing decisions and the Quality of Service (QoS) they offer. According to the SPs´ rationality level, we consider two schemes: 1) Both SPs are rational, and 2) One SP is rational and the second SP is boundedly rational. We describe the competitive interaction and analyze the resulting equilibria. Later, 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 equilibria (NEs). We prove that there exists exactly one NE which is fair whereas remaining equilibria are unfair. A special feature is that the stability condition of the Nash equilibrium coincides with the instability condition of the boundary equilibria. Thus the system would never be absorbed by any of the unfair equilibria which solves the equilibrium selection issue ! Moreover, we show that considering the delay case (i.e., assuming a market with memory) increases the stability of the system. Here, the size of the memory could be considered for multi-level rationality, which means that bounded rationality tends to rationality as the memory size increases. We finally show that boundedly rational SPs with delay have a higher chance of reaching the fair Nash equilibrium.