credit and



Economic context

The Internet, and more generally telecommunication networks, have progressively switched from an academic or monopolistic network to a commercial one with competitive service providers. In order to get a return on investment, each provider has to define a pricing strategy to charge users for the service they experience.

Pricing has at the beginning been seen as a way to cope with congestion, to control demand, to deal with and satisfy heterogeneous applications with different quality of service (QoS). It has also been regarded as a way to introduce fairness among users with respect to the traditional flat-rate pricing where light consumers pay as much as big ones. Therefore, there have been many proposals for new pricing schemes motivated by different objectives: the network planner may want to elicit users to efficiently share the scarce network resources in order to maximize social welfare, to guarantee fairness among users, or to maximize revenue; the typical modeling tool being that of non-cooperative game theory. A very large proportion of papers deal with the monopolistic case, where there is only one provider.

Though, telecommunication networks have become highly competitive and it seems primordial to us to deal with that competition in pricing models when defining the optimal prices, since competition may highly affect the results of price determination (while pricing in a monopolistic context generally means a single level of game between users, competition actually introduces an additional level of game, between providers, resulting in a so-called Stackelberg game). Some typical illustrations of competition are described below.

It is crucial to take into account the non-cooperation among service providers in nowadays networks, for it is well known that non-cooperation leads to a loss of efficiency, quantified by the so-called price of anarchy. Therefore evading the question of provider competition when studying pricing mechanisms leads in general to falsely optimistic conclusions. Indeed, a pricing mechanism that elicits consumers to efficiently use network resources may completely miss that objective when several providers willing to maximize profit are in presence: a price war (i.e. providers lowering prices to gain market shares) is very likely to occur and drive the system to a situation totally different from the one initially targeted by the pricing scheme.

Another issue is to study possible alliances/collusions of some providers with respect to others. What would be the gain for such providers? What is the impact on the others: are they going to experience a loss? Studying the impact on the overall social welfare is also of importance. In case of unfair results, it would be of interest to introduce incentives or regulation procedures to avoid such behaviors.

In nowadays telecommunication networks, competition among providers, and the relation to seamless access to networks and services, gave rise to a new (at this scale) phenomenon, called churn, that consists in consumers switching from one provider to another. This phenomenon has a considerable impact on network provider revenues due to its frequency: each year around 25% of the clients of an operator change to another provider. To prevent users from switching to another provider, operators can use retention strategies that have to be studied and sanctioned if they prevent an efficient use of the resources.

Scientific issues of the project

Our goal in this project is to introduce and analyze pricing models dealing with competition in the context of constantly evolving telecommunication networks and services. Several types of situations, with different technical (and therefore economic) implications, may occur. For example, in the case of competition between different technologies like 3G, WiFi and WiMAX, providers are being operated on different frequency channels and using different PHY modes, therefore the demand level for one type of access has not influence on the QoS experienced by users choosing other technologies. On the other hand, if we consider competition between several operators with the same technology, as for example at a WiFi hotspot, then the same radio spectrum has to be shared between all providers and users, and the interactions between all participants (providers and consumers) are more complex to study. Furthermore, the technical limitations like total capacity limits for all providers will have to be taken into account when studying the competition among providers for capturing consumers and therefore maximizing revenue.

With respect to that main problematic of competition among providers, we wish to address the following issues:

To treat those issues, we intend to introduce different mathematical models to highlight some particular phenomena, and solve those models using tools and methods from Game Theory and from optimization, areas in which we developed an expertise during previous works and projects.