Section: New Results

Network Economics

Participants : Bruno Tuffin, Jean-Marc Vigne.

While pricing telecommunication networks was one of our main activities for the past few years, we are now dealing with the more general topic of network economics (see for instance [83] ). We have tackled it from different sides: i) investigating how QoS or QoE can be related to users' willingness to pay, ii) investigating the consequences and equilibria due competition among providers in different contexts, iii) looking at the economics of applications, for example adword auctions for search engines, iv) studying the network neutrality issue, and v) the not so considered problem of search-neutrality.

On the first item, we have studied in [78] how utility functions can be related to QoE recent research. Indeed, a logarithmic version of utility usually serves as the standard example due to its simplicity and mathematical tractability. We argue that there are much more (and better) reasons to consider logarithmic utilities as really paradigmatic, at least when it comes to characterizing user experience with specific telecommunication services. We justify this claim and demonstrate that, especially for Voice-over-IP and mobile broadband scenarios, there is increasing evidence that user experience and satisfaction follows logarithmic laws. Finally, we go even one step further and put these results into the broader context of the Weber-Fechner Law, a key principle in psychophysics describing the general relationship between the magnitude of a physical stimulus and its perceived intensity within the human sensory system.

A notable part of our activity has been related to competition among telecommunication providers, mainly within the framework of the ANR CAPTURES project ending this year. The goal is to improve most of the pricing models analysis which only deal with a single provider while competition (that is observed in the telecommunication industry) can drive to totally different outcomes. A general view of some of our results is summarized in [77] . A general model of competition in loss networks is described and analyzed in [25] as a two-levels game: at the smallest time scale, users' demand is split among providers according to Wardrop principle, depending on the access price and available QoS (depending itself on the level of demand at the provider); at the largest time scale, providers play a pricing game, trying non-cooperatively to maximize their revenue. A striking result is that this game leads to the same outcome than if providers were cooperatively trying to maximize social welfare: the so-called price of anarchy is equal to one. In [59] , we present a similar model of competition on prices between two telecommunication service providers sharing an access resource, which can for example be a single WiFi spectrum. We again obtain a two-level game corresponding to two time scales of decisions: at the smallest time scale, users play an association game by choosing their provider (or none) depending on price, provider reputation and congestion level; at the largest time scale, providers compete on prices. We show that the association game always has an equilibrium, but that several equilibria can exist. The pricing game is then solved by assuming that providers are risk-averse and try to maximize the minimal revenue they can get at a user equilibrium. We illustrate what can be the outcome of this game and that there are situations for which providers can co-exist.

Network economics is not only about ISPs, it also deals with the application side. In order to make money, many service providers base their revenue on advertisement. Search engines for example get revenue thanks to adword auctions, where commercial links are proposed and charged to advertisers as soon as the link is clicked through. The strategies of the search engine and advertisers are described and analyzed in [24] .

A new issue on which most of our work has focused in 2012 is related to the network neutrality debate. This debates comes from the increasing traffic asymmetry between Internet Service Providers (ISPs), mainly due to some prominent and resource consuming content providers (Cps) which are usually connected to a single ISP. Thus the ISPs to whom those CPs are not directly connected have started to wonder why distant CPs should not be charged by them, with the threat of their traffic not being delivered if they do not accept to pay, or their quality of service decreased. In [79] , we have described and analyzed the respective arguments of neutrality proponents and opponents, and we have also participated to Inria's response to the ARCEP consultation on the topic [90] . We have reviewed in [50] , [85] the economic transit agreements between ISPs in order to determine their best strategy. We have defined a model with two ISPs, each providing direct connectivity to a fixed proportion of the content and competing in terms of price for end users, who select their ISP based on the price per unit of available content. We have analyzed and compared, thanks to game-theoretic tools, three different situations: the case of peering between the ISPs, the case where ISPs do not share their traffic (exclusivity arrangements), and the case where they fix a transfer price per unit of volume. The impact on the network neutrality debate is then discussed. An analysis with a hierarchy of providers, with separated backbone providers and access providers, is performed in [89] . We also remarked that while there have been many studies discussing the advantages and drawbacks of neutrality, there is no game-theoretical work dealing with the observable situation of competitive ISPs in front of a (quasi-)monopolistic CP. Though, this is a typical situation that is condemned by ISPs and, according to them, another reason of the non-neutrality need. We have developed and analyzed in [40] , [84] two different models describing the relations between two competitive ISPs and a single CP, played as a three-level game corresponding to three different time scales. At the largest time scale, side payments (if any) are determined. At a smaller time scale, ISPs decide their (flat-rate) subscription fee (toward users), then the CP chooses the (flat-rate) price to charge users. Users finally select their ISP (if any) using a price-based discrete choice model in [84] or following Wardrop principle in [40] , and decide whether to also subscribe to the CP service. The game is analyzed by backward induction. As a conclusion, we obtain among other things that non-neutrality may be beneficial to the CP, and not necessarily to ISPs, unless the side payments are decided by ISPs (through a non-cooperative game). Another specific scenario is studied in [51] , where the impact of wholesale prices is examined in a context where the end customer access both free content and pay-per-use content, delivered by two different providers through a common network provider. We formulate and solve the game between the network provider and the pay-per-use content provider, where both use the price they separately charge the end customer with as a leverage to maximize their profits. In the neutral case (the network provider charges equal wholesale prices to the two content providers), the benefits coming from wholesale price reductions are largely retained by the pay-per-use content provider. When the free content provider is charged more than its pay-per-use competitor, both the network provider and the pay-per-use content provider see their profit increase, while the end customer experiences a negligible reduction in the retail price.

If network neutrality has recently attracted a lot of attention, search neutrality is also becoming a vivid subject of discussion because a non-neutral search may prevent some relevant content from being accessed by users. We propose in [88] to model two situations of a non-neutral search engine behavior, which can rank the link propositions according to the profit a search can generate for it, instead of just relevance: the case when the search engine owns some content, and the case when it imposes a tax on organic links, a bit similarly to what it does for commercial links. We analyze the particular (and deterministic) situation of a single keyword, and describe the problem for the whole potential set of keywords. In [52] , we analyze one behavior that results in search bias: the payment by content providers to the search engine in order to improve the chances to be located (and accessed) by a search engine user. A simple game theory-based model is presented, where both a search engine and a content provider interact strategically, and the aggregated behavior of users is modeled by a demand function. The output of each stakeholder when the search engine is engaged in such a non-neutral behavior is compared with the neutral case when no such side payment is present.