Oligopoly competition in time-dependent pricing for improving revenue of network service providers with complete and incomplete information

Network traffic load usually differs significantly at different times of a day due to users' different time-preference. Network congestion may happen in traffic peak times. In order to prevent this from happening, network service providers (NSPs) can either over-provision capacity for demand at peak times of the day, or use dynamic time-dependent pricing (TDP) scheme to reduce the demand at traffic peak times. Since overprovisioning network capacity is costly, many researchers have proposed TDP schemes to control congestion as well as to improve the revenue of NSPs. To the best of our knowledge, all the studies on TDP schemes consider only the monopoly or duopoly NSP case. In our previous work, the duopoly NSP case has been studied with the assumption that each NSP has complete information of quality of service (QoS) of the other NSP. In this paper, an oligopoly NSP case is studied. NSPs try to maximize their overall revenue by setting time-dependent price, while users choose NSPs by considering their own time preference, congestion status in the networks and the price set by the NSPs. The interactions among NSPs are modeled as an oligopoly Bertrand game. Firstly, assuming that each NSP has complete information of QoS of all NSPs, a unique Nash equilibrium of the game is established under the assumption that users' valuation of QoS is uniformly distributed. Secondly, the assumption of complete information of QoS of all NSPs is relaxed, and a learning algorithm is proposed for NSPs to achieve the Nash equilibrium of the game. Analytical and experimental results show that NSPs can benefit from TDP scheme, however, not only the competition effect but also the incomplete information among NSPs causes revenue loss for NSPs under the TDP scheme.