Section: New Results

Pricing

Participants : Hai Tran Hoang, Hélène Le Cadre, Bruno Tuffin.

Pricing is probably one of the most efficient means to control congestion in a communication network. It is furthermore mandatory for service differentiation and is a way to yield incentives for participation in P2P or ad hoc networks. Our work in the area has focused on two aspects: the design and feasability of pricing schemes first, and more recently, the analysis of the behavior of those pricing schemes in the case of an oligopoly, with providers competing for customers or daling with inter-domain relationships.

We have therefore first looked at different ways to design a pricing schemes. In [21] , we have developped several schemes for pricing a RED buffer, where the drop probability (or more exactly the slope of the drop curve of RED) depends on the willingness to pay of the users: the more you pay, the less one of your packets is likely to be dropped. Learning techniques are used to drive the system to an equilibrium. As a general pricing principle, since there is usually no strict guarantee of QoS, we have designed in [26] a technique where a reimbursement is realized in case a QoS threshold is not met. We have compared it with the case without reimbursement and illustrated that it could drive to a higher revenue for a provider (because more users are likely to apply). In [41] , we have designed a pricing scheme specifically focusing on WiMAX, taking into account its performance characteristics.

But our activity around pricing has mostly been redirected towards competition issues among providers: the impact of this competition has to be carefully analyzed. In [43] , we have studied a pricing game when several WiFi providers compete for customers. In [51] , the game is played when customers churn, i.e., migrate between providers, the churn rates depending on the different prices, reputations or QoS levels. In [52] , we have analyzed a pricing game between a WiFi and a WiMAX providers, were the WiFi can adapt its transmission range to reach the most adequate part of the population. We have similarly studied in [53] the case where providers own a part of the spectrum but there is a remaining part which can be shared freely. The question we try to solve is: what is the best interest, in terms of social or user welfare, is it to licence or to unlicence the frequency band? What is the best trade-off? Another situation typical of current relationships between providers is the case where there are mobile network operators (MNOs) and virtual mobile network operators (MVNOs). The goal is to determine the best strategy both for MNOs and MVNOs in terms of investment or contract, and what are the regulation procedures that can be imposed to make the system viable [48] , [47] , [49] . A related work on regulation is [50] , where (using repeated game theory), we fix a limit on the interval before being allowed to change prices, in order to prevent collusion among providers.

Another important activity is around interdomain issues, where intermediate domains need some (economic in our case) incentives for forwarding the traffic of other domains. In [80] , we have described the problem, provided a state of the art and highlighted the difficulties that must be solved.

All the above models require to understand the behavior of customers facing price offers. In [20] , we have proposed a statistical method to represent users' preferences for bundles of offers from providers, in a competitive context. The goal is to propose the most profitable set of possibilities.