Optimal hierarchical pricing schemes for wireless network usage and resource allocation

Typically the cost of a product has many components. Various components correspond to the production chain steps through which the product goes before meeting a customer. This also takes place in the price formation in wireless networks. For instance, before transmitting customer data, a network operator has to buy some frequency range and also establish contracts with electricity providers. In this paper we try to establish the tariff formation scheme in wireless networks. We consider an hierarchical game with three levels: the user, the provider and the authority. The user intends to transmit data on a network. The amount of traffic sent by the user depends on the available frequency bandwidth as well as on the tariff. The amount of frequency bandwidth is negotiated between the provider and the authority. A natural question arises for the provider: which tariff the provider has to assign to get the maximal pure profit, i.e. different between how much he obtains from the user and how much he has to pay for the reserved frequency bandwidth to the authority. The authority also looks for the frequency bandwidth tariff which can bring a maximal profit for him. We consider a Stackelberg game model with three levels of hierarchy: the authority as the leader of the first level, the provider who is the follower for the authority and the leader for the lower level, and the user who is the follower for the provider. The formulas for optimal tariffs at each level are established and some very interesting properties of the equilibrium are investigated. The authority obtains more profit by reducing the bandwidth frequency tariff, meanwhile the provider achieves better profit by increasing the user’s rate tariff. In fact, our mathematical model can confirm the opinion that the telecom companies have payed too much for 3G licences. Finally, we note that the main novelty in this paper compared to the standard Stackelberg pricing games extensively investigated in the literature is that we consider the three level hierarchical structure user-provider-authority.