Section: New Results

Network Economics

Participants : Pierre Coucheney, Hai Tran Hoang, 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. 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 equilibrium due to competition among providers in different contexts, iii) studying the economic aspect of interdomain relationships, iv) looking at the economics of applications, for example adword auctions for search engines, v) investigating the economics of security in telecommunications, vi) studying the network neutrality issue.

On the first item, in [70] , [29] , we have studied 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 thas been related to competition among telecommunication providers, mainly within the framework of the ANR CAPTURES project. 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 [67] . A general model of competition in loss networks is described and analyzed in [22] as a two-levels game: at the smallest time scale, users' demand is split among providers according to the Wardrop principle, depending on the access price and avaliable QoS (depending itself on the level of demand at the provider), and at the largest time scale, providers play a pricing game, trying non-cooperatively to maximize their revenue. A strking 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. An additionial (higher) level of game is analyzed in [23] (but using another type of negative externality for users, based here on delay), at which providers play on the technologies to implement, based on the infrastructure and licence (if any) costs, anticipating what would be the resulting price war outcome and revenue for given profiles of sets of technologies. This type of study may help a regulator to decide a licence cost, in order to drive the resulting Nash equilibrium to a better point in terms of social or user welfare. A specific situation we have analyzed is the case for a competitive market operated by a Mobile Network Operator (MNO) and a Mobile Virtual Network Operator (MVNO) [46] . The resource that is leased by the MNO to the MVNO is spectrum. MNO and MVNO compete posting subscription prices and the mobile users may choose to subscribe to one operator, or not to subsrcibe. The scenario is modeled by a three-level game comprising: a bargaining game, which models the spectrum leasing by the MNO; a competition game, which models the price competition between the MNO and the MVNO, and a subscription game, which models the subscription choice by the mobile users, and the outcome of which may be either not to subscribe, to subscribe to the MNO or to subscribe to the MVNO. We assess which conditions lead to an equilibrium where the competition does take place and the amount of the spectrum that should be leased to maximize user or social welfare.

Another important activity is around interdomain issues, with a network like the Internet being made of thousands of autonomous systems. Intermediate domains need some (economic in our case) incentives for forwarding the traffic of other domains. In [33] , we have described the problem, provided a state of the art and highlighted the difficulties that must be solved. In [32] , we have designed a decentralized algorithm based on double-sided auctions to allocate (and charge) the resource usage.

But 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. Most search engines have chosen (or switched to) a revenue-based ranking and charging scheme instead of a bid-based one. In [53] we investigate the relevance of that scheme when advertisers' valuation comes from a random distribution, showing that depending on the search engine's click-through-rate, revenue-based does not always outperform bid-based in terms of revenue to the search engine. But in this adword auction context too, there exist very few works dealing with serach engines in competition for advertisers. We have developped a two-level game where at the largest time scale search engines decide which allocation rule to implement, between revenue-based and bid-based; and at the lowest time-scale advertisers decide how to split their advertising budget between the two search engines, depending on the benefits this will bring to them. The game at the largest time scale is solved using backward induction, the search engines anticipating the reactions of advertisers [54] , [52] . We describe the advertisers best strategies and show how to determine, depending on parameters, an equilibrium on the ranking rule strategy for search engines; this may explain Yahoo!'s move to switch from bid-based to revenue-based ranking to follow Google's strategy.

We similarly have looked at the competition aspects linked to security. We have reviewed the interactions and strategies of attackers and defenders [68] . But we have also looked at the economics of network security, when network users can choose among different security solutions to protect their data, offered by competitive security providers [51] . The interactions among users are modeled as a noncooperative game, with a negative externality coming from the fact that attackers target popular systems to maximize their expected gain.

A new issue we are investigating is the network neutrality debate coming from the increasing asymmetry between Internet Service Providers (ISPs), mainly due to some prominent and resource consuming content providers which are usually connected to a single ISP. We have described and analyzed in [69] the respective arguments of neutrality proponents and opponents, and are currently completing the analysis of several promising game-theoretic models on this issue.