Competition Among Providers for Telecommunication Users: Rivalry and Earning Stakes

- How to characterize the equilibrium in the distribution of customers among providers? Does it exist and is it unique? There are several classes of demand functions used for instance in the marketing, industrial organization and transport literature. They have to be adjusted to the set of offered service and prices.
- A first way to represent demand repartition is from transport theory, which is closely related to telecommunication modelling. In that case, each packet is like a car on a road, and its influence on the resulting traffic can be seen as negligible. Then demand will be split in such a way that for each route (at each provider), the perceived cost, made of the charge imposed on customers and the level of QoS provided, will be equal for each provider receiving some traffic. Indeed, otherwise part of the traffic could be re-routed to a “cheaper” provider. The resulting equilibrium is called a Wardrop equilibrium. This kind of model has already been carried out with success by the partners to represent providers with limited bandwidth in competition for customers in a slotted allocation game, such that demand in excess at each slot is lost. This could represent providers on different platforms in competition (for instance WiFi against WiMAX against 3G…).
- In the previous case though, demand is somehow fixed (or known) to reach the equilibrium. This assumption generally has to be relaxed to deal with uncertainty. Attraction models, coming from marketing theory, could be other valuable representation tools. In that case, given a potential market size, a market share is proportional to an attraction value, depending again on price and delivered QoS. A special class of attraction model is the well-known (generalized) MultiNomial Logit (MNL).
- Linear demand functions with uncertainty/variability in the demand (expressed as a random variable) as opposed to the fixed (and usually linear) demand in the Wardrop model explained above can also be used. The implications of uncertainty have to be carefully analysed.
- Log-separable demand functions where demand is represented by a general function of prices, multiplied by a scaling function depending on QoS levels.

- A comparison of these modelling assumptions has to be realized, and the impact on the second level of game has to be studied. Is there a Nash equilibrium in the war between providers? Recall that a Nash equilibrium is a vector of providers’ strategies such that no provider can improve its revenue by unilaterally changing its own strategy. If it exists, is this equilibrium unique and what can drive the system to a “good” one? This kind of study exists for inventory models, but it has to be performed for telecommunication network access. We need here to address the technological specificities of wireless 3G (CDMA) networks, WiFi, WiMAX, ADSL, FTTx… Those specificities will be explicitly described in the delivered QoS depending on demand repartition. Then, are the conclusions robust to demand distribution assumptions? What is the most relevant one otherwise? This study seems to us an important point to validate the modelling conclusions.
- Providers in direct competition for customers, where the QoS level is represented by the delay experienced at each provider (directly depending on local demand). Such a model was studied, but only when demand distribution follows Wardrop’s principle.
- A second kind of game representing some networking contexts is that of a slotted game where each provider has a fixed capacity during each time slot, and a fixed access price. Each provider serves its demand up to its capacity, demand in excess being dropped. Slotted games are representative of many wireless systems. Here again, the analysis performed was for a fixed demand explained by Wardrop’s principle.
- We will first look at the case where providers play simultaneously on their price and capacity.
- A typical situation is when they can lease part of a network or when the network can be shared by providers. An illustration of the latter point is in 3G wireless networks, where, in order to get a higher utilisation, new models are being developed such that the radio spectrum unused by some providers could be actually used by others.
- Another interesting situation is also when some compensation for leasing part of its own network is provided (typically how some wireless providers, i.e. M6 mobile, Virgin Mobile…, arrived, by renting their network to incumbent ones, creating virtual networks). What is the resulting equilibrium, and is there any incentive to lease rather than directly sell to customers?

- Providers can also play in two steps: first they choose the capacity they want to offer (at a given cost), and then when all capacities are advertised, they play the price war. This game may be representative of situations due to different time scales: providers invest first for a given capacity or QoS level, and can then play on prices. We therefore have a three stage game with three different time scales: on capacity, then prices, and then demand distribution. As we have seen, the strategy developed at the price setting level depends on the demand distribution. Similarly, the provider’s best strategy in the game on capacities is to gain from knowing about the equilibrium his choice would drive to in the price game.
- A comparison of the two games will also be interesting. Do they lead to similar results? Whatever the answer, what is the interpretation?
- Is there an impact of alliances on capacity planning of some providers?
- A next issue is to look at the capacity investment on a longer term. Given that (typically the wired contexts) costs for capacity expansion decreases when time passes, when is the right moment for investing in additional resources, especially in this competitive context? Some mathematical models, mainly based on diffusion theory, exist in the literature [4], but a simpler model, with more basic assumptions, will need to be considered here to integrate competition on price and the different games.
- In the case of FTTx, where installation cost almost not related to the planned capacity, what is the incentive for providers to over-provision their network? Shouldn’t they voluntarily offer a insufficient capacity for justifying higher prices because of congestion? The competitive context is of importance in this kind of analysis.
- What does “use the network efficiently” mean? This question refers to the notion of a global efficiency measure, which we have to properly define, and which will be used to compare different outcomes from a global perspective. Depending on the aspects we wish to emphasize (performance, user satisfaction …), we can imagine different definitions of that measure, depending on the approach we consider.
- One possible approach corresponds to an engineer’s view of the problem, who would like the network to carry as much information as possible, taking into account the feasibility condition (capacity limits). A possible definition of the efficiency metric in that context can be the total network throughput, or the load repartition among the different links (with the objective to control load balancing), or other measures to minimize like the total amount of lost traffic, or the total delay of transmitted packets.
- We can also prefer to use metrics that are more economics-oriented, by choosing for example Social Welfare, which is the sum of the values that an outcome has for all the participants. Some other metrics can also consider fairness issues, or include providers’ revenue considerations.

- Does competition among providers lead to a bad use of the network? For each competition model we will consider, our first step will therefore be to determine the Nash equilibria (if any), and to compute the optimal value of the efficiency metric by considering perfect coordination (“optimal” situation). Comparing the efficiency values obtained for those outcomes will quantify what is lost due to participant selfishness. If the price of anarchy is large, then some means will have to be found to force or elicit coordination among the participants of the game.
- If competition leads to an inefficient use of the network, how to improve this? Since it is unreasonable to assume that a central administration may control all the participants of the game or impose each provider its exact behaviour, we will focus only on the limited tools that can be introduced to reduce the price of anarchy. We may consider two different types of mechanisms to change the rules of the game played by participants and therefore influence its outcomes.
- It is possible to introduce strict constraints to providers and/or consumers, for example by imposing a minimum or maximum selling price for the service, or imposing strict requirements in terms of QoS, of network use, etc. Finding the equilibria of such games will imply constrained optimisation, that we intend to solve analytically if possible, or eventually numerically if the models are intractable.
- It should be easier to study other types of mechanisms, based on incentives: instead of controlling that the behaviour of each provider is conformant to some fixed constraints, a regulator can let providers behave the way they want, but add some rewards or penalties to those that behave in a proper way or not. The more natural kind of incentives are monetary: by playing on taxes and/or subsidies, the regulator can elicit the revenue-driven providers to modify their behaviour. From a mathematical point of view, determining the equilibria of such modified games involves tools from continuous optimisation, and does not add constraints. It can therefore be easier to do than for strict enforcement mechanisms.

- A first typical situation is that of two operators using different technologies. One could be WiMAX while the other operates WiFi. WiMAX can reach customers at a much longer distance than WiFi, and therefore runs a larger coverage area. We can then think of a provider enduring competition on a fraction only of his customers, since the other part is not reachable from the concurrent. What is then his best strategy in terms of price setting? Shall the (WiMAX) provider compete for demand on the common market, or shall he just leave it to the (WiFi) concurrent and concentrate on revenue on the monopolistic area? Here again, a non-cooperative game analysis has to be carried out. The general methodology to solve this problem is similar to the one of WP1, but with additional variables.
- In most of the games highlighted before, providers have their own capacity that they want to sell. Though, there are many situations where providers share the capacity (partially or not). A typical situation is WiFi. Indeed, we are more and more accustomed to see several WLAN providers coexisting in a public WiFi hotspot to provide wireless access services for the same group of users. In attempting to attract users and extract the full revenue potential of service, WLAN providers need to provide services and set prices by taking into account a wide range of factors, including preferences of end-users, the QoS and cost limitations of used technology, 802.11 system, and the potential competition from other services providers. Here providers use the same radio spectrum and one provider serving a large number of customers reduces the capacity of concurrent providers. This externality on capacity has to be taken into account and generates again a different game to be analysed.
- Providers might also be interested in offering service differentiation. For instance, there may be a priority for customers who pay more. Many pricing schemes for service differentiation have recently been designed for telecommunication networks because of users/applications with heterogeneous QoS requirements (video requires large bandwidth and small delay while email requires no loss but tolerates small bandwidth and delays). On the other hand, almost no analysis of the feasibility of those multi-class schemes under competition has been carried out. Our goal is to study the scenario where at least one provider proposes different classes. How is demand split again? In the price game, does the provider have an interest in really offering service differentiation?
- What is the best strategy for each provider in terms of retention strategy and in terms of price? This induces again a game since the behaviour of customers, and therefore the revenue of each provider, will depend on the whole market picture (churning rates…). Is there a Nash equilibrium, and if so, is it unique? Again, this can be studied in several cases: providers may just play with retention delay, with prices, or both.
- What are the regulation possibilities for a governmental authority to prevent providers from retaining too much their customers? A basic way to proceed is to define sanctions if the retention delay is large. Determining threshold fees under which sanctioning is useless will be carried out with the help of our model.

**Leader: Bruno Tuffin (INRIA)**

**Leader: Mustapha Bouhtou (FT R&D)
Participants: FT R&D, INRIA, TELECOM Bretagne**

The central goal of this project is to study competition among providers. Indeed, a very large proportion of papers deal with the monopolistic case, where there is only one provider. Though, telecommunication networks have become highly competitive. As a consequence, the behaviour, efficiency and survivability of pricing models seeming adequate in the monopolistic case has to be investigated in a competitive environment, because it may lead to opposite results. A primary result illustrating this kind of problem is the promising so-called Paris Metro Pricing (PMP) scheme, consisting simply in separating the network in logically different sub-networks with different prices but served exactly in the same way (therefore most expensive networks should be less congested ) is not viable under competition. Studying the impact of competition is therefore a central issue.

We thus have to represent each competition pricing as a Stackelberg (two stages) game. In a first step, depending on the offered QoS and the price at each provider, demand is split among providers. In a second step, based on this knowledge, providers play a game on prices (and can additionally play with capacity, QoS and other parameters) in order to maximize their revenue. Those two games are strongly dependent: the way demand is distributed depends on prices set by all providers; similarly the price strategy of a provider will depend on demand distribution. What complicates more, even at the first step, demand depends on QoS, itself depending on the number of attracted customers. WP1 discusses adequate models for distributing demand, and their implications on the resulting game among providers. We will answer the following questions:

Some key and representative models will be considered for this study, but depending on time more case studies could be added. Those models of interest are:

The modelling tools that will be used in this work-package are non-cooperative game theory tools, discrete choice models and optimization. The partners have acquired a strong knowledge on those tools thanks to their previous works on the development of pricing schemes in telecommunication networks. Their knowledge in networking, being wired or wireless, will also be of high interest to properly represent the different technologies and the QoS stemming from the actual demand.

**Leader: Bruno Tuffin (INRIA)
Participants: FT R&D, INRIA
**

While price war is studied by WP 1, we believe that associating to the game on prices, where providers’ strategies are to set the price to access their network, a game on capacities or more generally on QoS, will be more representative of providers’ real problem. In this situation, there is a cost for getting additional capacity or providing a better QoS, and this has to be weighted with the revenue this brings to the provider. Two different situations can be imagined and will be considered in this WP:

The basic tools used in this WP are the same than in WP 1, i.e., non-cooperative game theory and optimization.

**Leader: Patrick Maillé (TELECOM Bretagne)
Participants: FT R&D, TELECOM Bretagne
**

As illustrated by the famous Prisoner’s dilemma, it is well known from Game Theory that the conjunction of selfish decisions will not necessarily be globally optimal, and indeed can be worse for every participant of the game that some other possible outcome. However, by nature networks involve a very large number of actors of several kinds (consumers, providers, brokers), with diverging interests, so it is unreasonable to suggest that the network be centrally controlled to improve its efficiency. Therefore, the loss of efficiency due to selfish behaviours of actors cannot be ignored. This loss can be quantified by the so-called Price of Anarchy, defined as the worst-case ratio comparing the global efficiency measure (that has to be chosen) at an outcome of the noncooperative game played among actors, to the optimal value of that efficiency measure. For routing games in transportation, some promising results have been recently obtained with the total transit time in the network as the measure of efficiency: it has in particular been proved that the price of anarchy can be bounded independently of the network topology and of the network demands over origin-destination pairs over the network. If the price of anarchy is not too large, then this suggests that the system is run close to the optimum without the need for any coordination. Otherwise, some tools should be used to limit the efficiency loss (via the introduction of incentives in the network).

It appears momentous to us to study the price of anarchy in the context of the competition models we will propose, in order to evaluate the overall impact of the interactions between all agents involved in the network. We wish to answer the following questions:

**Leader: Patrick Maillé (TELECOM Bretagne)
Participants: INRIA, TELECOM Bretagne
**

While previous work-packages deal with competition issues in telecommunication network at a quite macroscopic (but relevant) level, we would like to investigate some specific scenarios for which the analysis will be different. Three particular cases will specifically retain our attention:

**Leader: Mustapha Bouthou (FT R&D)
Participants: FT R&D, INRIA, TELECOM Bretagne
**

Our models are based on the assumptions that demand can easily migrate from one provider to the other. Though, operators often include in their contracts delays before letting the customer leave. We propose to develop mathematical models in this work-package to analyse this churning issue and propose rules (sanctions) to keep providers from retaining their customers for too long.

Our proposition is to design a mathematical model, more precisely a Markov chain that will represent the behaviour of customers facing the contracts offered by providers. The transition rates of the Markov chain depend on the respective delays before being allowed to leave a provider, their reputation, and possibly many other parameters. Customers are also allowed to change their mind and finally stick to a provider after thinking of switching (win-back model). Based on the steady-state behaviour of the Markov chain, the different issues that have to be solved are:

Getting steady-state values for the behaviour of customers will be easily obtained thanks to standard Markov chain theory. Our goal is then to investigate the existence of Nash equilibria. We expect to get analytical results (i.e. closed-form expressions), but in the case where the utility functions representing providers’ benefits are too complicated in terms of the parameters of interest, extensive and careful numerical analysis can at worst be obtained. Similarly for optimizing the regulation strategy, we will obtain at best analytical results, at worst, a numerical optimization.

The other regulation issue we propose to tackle is related to alliances/collusions that happen in some contexts. We would like to design regulation mechanisms incentivizing providers to avoid alliances. With several models of competition (depending on the technology), we will aim first at illustrating the gain of providers members of the alliances and the potential loss of rivals and in terms of social welfare. Then designing rules (and maybe detection procedures) such that this kind of behaviour will be prevented.