Yann Busnel

Nuno Cruz

Denis Gillet

Adrian Holzer

Hugo Miranda

Reinventing Mobile Community Computing and Communication

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. MOTIVATION

Application development for mobile devices has been following a sub-optimal and predictable pattern that consists in replicating, for the wireless setting, the services that have for long been available on wired desktops. Examples are distributed games and ubiquitous interaction with social networks. A few remarkable exceptions include travel assistants, which use information made available from mobile device sensors (in particular, from GPS receivers) to facilitate user mobility [START_REF] Raptis | Context-based design of mobile applications for museums: a survey of existing practices[END_REF]. Although this approach improves user productivity and satisfaction, it falls short of the expanding range of possibilities that the increasing computing power, networking capabilities and sensors integrated in mobile devices make available.

A. Advanced Social Networking Apps (SNAPPs)

In our vision, mobile devices should become effective human assistants, reacting to the events observed in the environment that are relevant to the user by offering advanced mobile context-dependent Social Networking APPlications, henceforth called SNAPPs. In order to motivate our vision, we present below two scenarios that make use of SNAPPs.

Scenario 1: Bob is visiting a shopping mall in a foreign city. While walking, Bob's smartphone receives a number of messages from other smartphones, indicating their user's Authors are listed in alphabetic order movements. Bob's smartphone is not familiar with the location and simply registers that the location is crowded and users tend to move. However, smartphones more familiar with the location notice that the movement pattern is unusual, given that all users in some region are moving in the same direction at an above average speed. As a result, they start sending alert signals both to their users and to other smartphones using their radio interfaces. Due to the large number of alert signals, Bob's smartphone suggests him to move away from the location, a few minutes before the fire alarm is triggered. Unfortunately, Charlie -an independent senior citizen -is currently in the mall and his health monitor notices a change in his condition, probably due to the panic. As a result, Charlie's smartphone places an automatic call to the emergency services, providing all the details about Charlie's health condition and location. After confirming the need for assistance, the smartphone mediates the communication between the emergency services, guiding them to Charlie's precise location. Moreover, the smartphone also finds a doctor currently in the flow of evacuating people, which provides assistance until the arrival of the emergency services.

Scenario 2: Alice and her son Tommy are at the amusement park when all of a sudden, Tommy disappears. After calling for help, Alice uses the emergency search app on her cell phone to spread a picture of Tommy that she had taken earlier. An alarm with the picture is gossiped in the background by the smartphones at the park, who start to look for Tommy in photographs shot by the devices recently. However, because face recognition is CPU intensive, smartphones extract faces from the photographs and delegate the facial recognition process to other smartphones in the neighbourhood with spare CPU time, effectively sharing the load and speeding up the process. In addition, some of the smartphones alert their users, thus creating a surveillance net set to increase every 5min. The picture is equally delivered to autonomous robots in the park who use real time face recognition software to try to find Tommy. Chloe, an autonomous robot who has received the picture, recognises Tommy and notifies Alice through the emergency app, telling her where to pick up Tommy.

The applications above have in common the emergence of a spontaneous collaborative system, composed by the mobile devices co-located in some region of interest. To be useful, these applications require a significant amount of computing power, operate in the background monitoring the environment (in Scenario 1) or waiting for some event (Scenario 2), but in any case without disturbing the users' other activities. In addition, applications will be required to share a large amounts of raw or preprocessed data, that is either stored or produced at the mobile devices, whose relevance is constrained to the location of the devices and whose exchange either between the devices or with a wired third-party is incompatible with the state-ofthe-art infrastructured networks. The following section makes a more in-depth discussion of the limitations that the current trend on application development and infrastructured wireless networks pose to the successful deployment of SNAPPs.

B. Limits of Current Systems

The development of a computing environment capable of supporting these applications is challenging due to a combination of factors that include the limited computing power and energy available at each mobile device, the lack of support to infrastructureless (ad hoc) networking on mobile operating systems, the large amount of context data and privacy constraints. Furthermore, the direction in which the state of the art on application development for mobile devices is moving is at odds with some fundamental principles needed to develop SNAPPs, given that, for example, it has been preferring pointto-point communication between the devices and servers on the wired infrastructure over device to device communication. Unfortunately, this raises a number of barriers as for cost, privacy and scalability issues, devices rarely communicate their sensor value in the wild.

Research that aims to extend the computing power of mobile devices can be broadly arranged in four classes, differentiated by the location where it is made available. The most popular approach makes the delegation visible for applications, which are required to explicitly perform remote calls to cloud hosted servers. This is the case of, for example, travel assistants and voice recognition applications. A second class uses the available infrastructure to delegate the computing power on resourceful servers executing virtualised versions of the mobile devices (e.g., [START_REF] Chun | Augmented smartphone applications through clone cloud execution[END_REF], [START_REF] Huerta-Canepa | A virtual cloud computing provider for mobile devices[END_REF], [START_REF] Cuervo | Maui: making smartphones last longer with code offload[END_REF]).

Cloudlets, on the other hand, avoid the latency involved in transferring state to and from the virtualised servers by placing the computing power on specialised devices in the vicinity of the wireless network [START_REF] Satyanarayanan | The case for vm-based cloudlets in mobile computing[END_REF]. The fourth class attempts to distribute the computing power among the mobile devices in proximity. In this paper, we claim that this is the preferable approach as it alleviates bandwidth on long range wireless links and mitigates privacy issues. Unfortunately, instantiations of this approach rely on mechanisms that do not take into account the particularities of the wireless setting (by using resource hungry frameworks like MapReduce [START_REF] Marinelli | Hyrax: Cloud computing on mobile devices using MapReduce[END_REF], or others [START_REF] Borcea | Cooperative computing for distributed embedded systems[END_REF], [START_REF] Murray | The case for crowd computing[END_REF]) and do not propose useful mechanisms to cope with the large amounts of data that must be transferred between the devices. Therefore, unless there is a dramatic paradigm shift, SNAPPs will not be part of our daily life anytime soon.

C. Towards a paradigm shift

In this paper, we present a research agenda divided in four distinct, yet complementary, research streams that aims at achieving a paradigm shift to produce an environment where SNAPPs can thrive. As depicted in Fig. 1, streams can be mapped on building blocks, each providing one class of services to the others and to SNAPPs and that put together different research areas. Each stream is presented in a distinct section as follows: Connectivity: Section II gives an overview of how Mobile Ad Hoc Networks (MANET) connectivity needs to be rethought in order to provide the adequate building blocks for message exchange between mobile devices. The section makes the case for the promotion to first class citizens of communication models whose properties are in general neglected like anycast, geocast and content-based publish-subscribe.

Databases: Section III gives an overview of distributed data storage issues and shows how database systems could be rethought in order to accommodate the huge amount of decentralised data that needs to be stored for SNAPPs. We aim for the implementation of a location dependent distributed database model, providing the insertion, retrieval, update and interpretation of information. Ideally, the database should support efficient retrieval and inference of information using data streams.

Computing: Section IV gives an overview of the issues related with the limited computing power available on mobile devices and proposes to rethink distributed computing in order to facilitate delegation of computing tasks to idle mobile devices nearby.

Applications: Section V reflects on application design and how incentive systems must be rethought to encourage adoption of SNAPPs. Namely, the use of bartering schemes, reward mechanisms and privacy enforcement to foster collaboration is discussed.

For each stream, the paper formulates a few research questions that raise light on the open issues that must be addressed in order to achieve this paradigm shift.

II. RETHINKING MANETS CONNECTIVITY

Network connectivity and low level messaging are the cornerstones of any distributed architecture. It is therefore essential to assess its potential limits and opportunities for SNAPPs.

Network support to SNAPPs is expected to exhibit two fundamental characteristics. One is the capability to detect other devices in proximity. The other is broadband, to make possible the exchange of the large amounts of data required by the applications. Unfortunately, none is provided by current infrastructure-dependent wireless technology. Infrastructure, in particular 3G and 4G, prevents bandwidth reuse in short distances, what reduces the number of simultaneous broadband connections and increases their cost.

Infrastructure-less networks, usually named ad hoc networks, are self-organised networks exclusively composed by the participating devices and could play a relevant role in short range communication. However, most of the research on ad hoc networks was concentrated on solving the problems raised by mirroring the TCP/IP communication stack on mobile devices. The large amounts of broadcast (e.g. [START_REF] Miranda | A poweraware broadcasting algorithm[END_REF], [START_REF] Garbinato | Context-aware broadcasting approaches in mobile ad hoc networks[END_REF]), point-to-point routing (e.g. [START_REF] Perkins | Ad hoc On-Demand Distance Vector (AODV) Routing[END_REF], [START_REF] Johnson | DSR: the dynamic source routing protocol for multi-hop wireless ad hoc networks[END_REF], [START_REF] Clausen | Optimized Link State Routing Protocol (OLSR)[END_REF]) and unique addressing protocols (e.g. [START_REF] Baccelli | IP Addressing Model in Ad Hoc Networks[END_REF], [START_REF] Jeong | Study on address allocation in ad-hoc networks[END_REF]) investigated during the last decade, aiming to a number of arguably usable scenarios, supports this claim. In contrast with MANETs, this issue was addressed and resolved in sensor networks and vehicular ad hoc networks (VANETs). In the former by having communication protocols to trade off a full blown stack by energy performance (see [START_REF] Anastasi | Energy conservation in wireless sensor networks: A survey[END_REF] for a survey). In the later by inserting parallel communication stacks along with TCP/IP to support particular applications such as short messaging [START_REF] Hartenstein | A tutorial survey on vehicular ad hoc networks[END_REF].

Point-to-point is only one of the communication models that should ideally support SNAPPs. Locating devices with idle CPU cycles, listening to movement direction announcements or delivering an image to some of the devices in proximity are all examples of services not adequately supported by point-to-point reliable delivery. In practice, this implies the definition of new communication paradigms that extend and refocus research on ad hoc networks, challenging the role of the TCP/IP communication stack in these networks and making other self-organised paradigms like epidemic dissemination, anycast and publish-subscribe, first class citizens of ad hoc networks. Removing the TCP/IP communication stack limits application, however it paves the way into a rupture with known communication paradigms. Most of the past attempts to remove or reinvent TCP/IP for ad hoc wireless environments have failed to be accepted by the community (e.g. [START_REF] Liu | ATCP: TCP for mobile ad hoc networks[END_REF], [START_REF] Sundaresan | ATP: A reliable transport protocol for ad hoc networks[END_REF]), however if the dismissal of TCP/IP is driven by the application, a good outcome should be expected. A precise identification of the paradigms to be supported will mostly depend of the computing and database requirements and therefore, is left as an open research question.

RQ 1 -What communication paradigms should be provided to support SNAPPs?

Early implementations of these novel communication paradigms for MANETs made extensive use of flooding, an algorithm that consists in having all mobile devices to retransmit the message once. Unfortunately, network interfaces are known to be one of the most power demanding components of mobile devices [START_REF] Feeney | Investigating the energy consumption of a wireless network interface in an ad hoc networking environment[END_REF] and the use of flooding further amplifies the problem. Luckily, work is underway to devise more efficient implementations (see for example [START_REF] Miranda | A poweraware broadcasting algorithm[END_REF], [START_REF] Pu | Enhanced blocking expanding ring search in mobile ad hoc networks[END_REF]) of these paradigms. However, the performance of these implementations depends on several variables like network topology, node density and number of messages. A crucial aspect to foster user adherence to SNAPPs, and which is raised in RQ 2, is that SNAPPs must be perceived as providing a benefit that compensates the cost of the decreased availability of the mobile devices due to the additional battery consumption.

RQ 2 -Will energy consumption prevent a wide adoption of SNAPPs? Should SNAPPs be available only in the less energy demanding scenarios?

The effort to improve power consumption on MANETs contrasts with the simplicity (from a mobile device perspective) of its implementation when the support of an infrastructure is available. In the later, mobile devices would be required to send a single point-to-point message with the data and the communication paradigm headers to the infrastructure, who would be responsible for enforcing the required communication properties and deliver it to the destinations. However, this model is not free of costs. Elsewhere [START_REF] Balani | Energy consumption analysis for bluetooth, wifi and cellular networks[END_REF], it was shown that transmissions using the cellular networks interface consume more energy than WiFi and Bluetooth. In addition, implementing these communication paradigms in infrastructure supported networks would require a stronger knowledge of the network, what could not be achieved without frequent message exchanges between the infrastructure and the mobile devices. Question 3 addresses these issues by seeking the borderline cases where the use of an infrastructure would be preferable.

RQ 3 -In which application scenarios and topologies will the use of infrastructure-based implementations of novel communication paradigms provide a more efficient usage of the device's batteries?

III. RETHINKING DISTRIBUTED DATABASES

To further increase the interoperability of SNAPPs, smartphones would be required to understand and learn from the messages circulating on the wireless broadcast media. Message interpretation can be supported by the definition of an ontology. However, in spite of existing efforts, it is hard to define an ontology encompassing all possible events and knowledge relevant in the scope of users' everyday activities. Therefore, message interpretation must be complemented with the ability to infer information simply from the message patterns and by the presence or absence of the messages. A similar behaviour can be found in Nature, where a limited set of sounds, smells or pheromones is used to implement a basic language that permits to communities of bees, wolf packs, etc. to alert all its members of eminent danger and organise the community.

Research should be focused in the support of "ether" knowledge bases by providing interfaces for insertion, retrieval, update and inference (using data streams) of information on location dependent databases. A possible solution focuses on continuous queries and streams, which rely on large-scale distributed information systems with decentralised management and avoid single points of control and failure. Within the system, each participant contributes with some physical resources (storage, computation, communication) and information composed of both data and queries. Data as well as queries, which are submitted to the system, are revealed to authorised participants who can then analyse them. This clearly improves information symmetry. Furthermore, participants interested in similar queries could take advantage of this knowledge to organise themselves to acquire necessary information, compute the query (as volunteer computing [START_REF] Anderson | Boinc: A system for public-resource computing and storage[END_REF]), store and disseminate the results. Hence, the more interested users there are for a query, the more resources are devoted to the query, the cheaper it is for a given participant to obtain results and the more the results are replicated and available.

A. Query and indexation

The organisation of participants may be leveraged through a flexible analysis of relations between the queries they issue. This relies on the definition of an algebraic formalisation as conducted in databases. For example, a simple "equivalence relation" permits to share the cost of a query evaluation through relevant reuse of results. Other more complex relations involving queries and sub-queries have to be studied to avoid repeated evaluations. Each considered relation leads to specific organisation, but they all share the general principle of organising participants accordingly to their queries. To sketch the general picture, a potential solution should be composed of two layers. The first one enables accessing and querying data with a simple language and offers basic data indexing capabilities. The second layer takes advantage of both distribution and algebraic analysis of queries to bring back the full power of querying to the users. They are freely developed using any kind of query language and tools without any limitation as far as they have access to basic information (data or queries). Moreover, many users may share enough resources to compute very complex queries which are currently out of their individual scope. Recent research has demonstrated the effectiveness of epidemic protocols in a variety of settings [START_REF] Haas | Gossip-based ad hoc routing[END_REF], [START_REF] Jelasity | Gossip-based peer sampling[END_REF], [START_REF] Riviere | Gossip-based networking for internet-scale distributed systems[END_REF]. These include not only traditional peer-to-peer applications such as data dissemination or overlay maintenance, but also user-oriented tasks such as identifying communities with similar interests, or recommendation systems. Still, an open research question is:

RQ 4-How can group communication paradigms contribute to perform efficient queries on such alternative infrastructure? How can data and users be efficiently organised? B. Stream analysis

In the applicative contexts of SNAPPs, it may be necessary to quickly and precisely process a huge amount of data. The problem of extracting pertinent information in a data stream is similar to the problem of identifying patterns that do not conform to the expected behaviour, which has been an active area of research for many decades. Unfortunately, a common feature of these techniques is their large space complexity and their computational cost, as they rely on full space algorithms for analysing their data. Given our settings -the real time monitoring of ad hoc network traffic -relying on full space algorithms for analysing input data is not feasible. In contrast, two main approaches exist to monitor in real time massive data streams. The first one consists in regularly sampling the input streams so that only a limited amount of data items is locally kept [START_REF] Subhabrata | Sketch-based change detection: Methods, evaluation, and applications[END_REF], [START_REF] Karamcheti | Detecting malicious network traffic using inverse distribution of packet contents[END_REF], [START_REF] Lakhina | Mining anomalies using traffic feature distributions[END_REF]. This allows to exactly compute functions (metrics, pattern matching, etc.) on these samples. However, accuracy of this computation, with respect to the stream in its entirety, fully depends on the volume of data that has been sampled and their locations in the stream. On the other hand, the streaming approach consists in scanning each piece of data of the input stream on the fly, and in locally keeping only compact synopses or sketches that contain the most important information about data items. This approach permits to derive some data streams analyses with guaranteed error bounds without making any assumptions on the order in which data items are received at nodes (i.e., data items ordering can be delayed by the ad hoc routing scheme [START_REF] Anceaume | Uniform and Ergodic Sampling in Unstructured Peer-to-Peer Systems with Malicious Nodes[END_REF]). Most of the research done so far with this approach has focused on computing functions or statistic measures with error ε using poly(1/ε, log n) space where n is the domain size of the data items. These include the computation of the number of different data items in a given stream [START_REF] Flajolet | Probabilistic counting algorithms for data base applications[END_REF], [START_REF] Kane | An optimal algorithm for the distinct element problem[END_REF], the frequency moments [START_REF] Alon | The space complexity of approximating the frequency moments[END_REF], the most frequent data items [START_REF] Alon | The space complexity of approximating the frequency moments[END_REF], [START_REF] Charikar | Finding frequent items in data streams[END_REF], the entropy of the stream [START_REF] Chakrabarti | A near-optimal algorithm for computing the entropy of a stream[END_REF], or the relative entropy between one data stream and the uniform one [START_REF] Anceaume | An information divergence estimation over data streams[END_REF], [START_REF] Anceaume | Ankle: Detecting attacks in large scale systems via information divergence[END_REF]. A comprehensive survey of these techniques, their advantages and their drawbacks is given in [START_REF] Chandola | Anomaly detection: A survey[END_REF].

Unfortunately, most of the work proposed for a single stream analysis is clearly not adaptable to the distributed functional monitoring model [START_REF] Cormode | Algorithms for distributed functional monitoring[END_REF]. However, a combination of sampling techniques and information-theoretic methods can be used to extract pertinent information from collections of streams (metrics, summaries, pattern matching, etc.). In this combination, the input data is read on the fly (as in the streaming model), and processed with a minimum workspace and time what makes it suitable for the combination of limited resources and broadcast medium of the SNAPPs environment.

In the communication complexity model, each node receives an input data stream, performs some local computation, and communicates only with a coordinator who wishes to continuously compute or estimate a given function of the union of all the input streams. The challenging issue in this model is for the coordinator to compute the given function by minimizing the number of communicated bits [START_REF] Cormode | Algorithms for distributed functional monitoring[END_REF], [START_REF] Arackaparambil | Functional monitoring without monotonicity[END_REF], [START_REF] Gibbons | Estimating simple functions on the union of data streams[END_REF]. Cormode et al. [START_REF] Cormode | Algorithms for distributed functional monitoring[END_REF] pioneer the formal study of functions in this model by focusing on the estimation of the first three frequency moments F 0 , F 1 and F 2 [START_REF] Alon | The space complexity of approximating the frequency moments[END_REF]. Arackaparambil et al. [START_REF] Arackaparambil | Functional monitoring without monotonicity[END_REF] consider the empirical entropy estimation [START_REF] Alon | The space complexity of approximating the frequency moments[END_REF] and improve the work of Cormode by providing lower bounds on the frequency moments, and finally distributed algorithms for counting at any time t the number of items that have been received by a set of nodes from the inception of their streams have been proposed in [START_REF] Haung | Randomized algorithms for tracking distributed count, frequencies and ranks[END_REF], [START_REF] Liu | Continuous distributed counting for non-monotonic streams[END_REF]. However, an open research issue is:

RQ 5-How can coordination be distributed among all participants of SNAPPs? How can on-line stream analysis provide inferred pertinent information dedicated to SNAPPs?

IV. RETHINKING DISTRIBUTED COMPUTING

To mitigate computing power shortage, current data management paradigm is moving more and more away from storing and processing data directly on the end device and delegating it to remote computer farms. This solution however is not sustainable, due to the physical limitations of wireless bandwidth which will eventually become a bottleneck for dataintensive communication. There is however an unexplored alternative solution which consists in using the idle storage space and computing power of surrounding mobile devices to store and process information, creating an ad hoc distributed computing environment.

A. Alternative Models

To be useful, this ad hoc distributed computing environment must outperform, either in latency or battery consumption, two alternative approaches: strictly local computation (LC) and delegation of the data on computer farms on the Internet (CF).

A comparison between the ad hoc computing environment and LC suggests that the parallelism that can be achieved by the former should improve performance. However, latency is affected by the need to coordinate the participants, in particular, to locate the peers, to deliver the data and integrate the results. In addition, ad hoc distributed computing is expected to be more power demanding (when measured by the integral over all the participating devices), as wireless bandwidth for message passing is also required.

Elsewhere [START_REF] Balani | Energy consumption analysis for bluetooth, wifi and cellular networks[END_REF], [START_REF] Perrucci | On the impact of 2g and 3g network usage for mobile phones' battery life[END_REF], it has been shown that long range wireless network interfaces like 3G or 4G consume significantly more power than short range like WiFi or Bluetooth. Therefore, the CF approach is expected to spend most battery on networking activities. The geographical distance between the smartphone and the servers as well as the limited bandwidth available on the long range wireless link (and which will be used to transfer data from the distributed database) are both expected to increase latency for CF.

Although the ad hoc distributed computing environment appears to be the most intuitive solution for obtaining computing power, it is not clear if ad hoc computing is capable to compensate the costs and latency of CF and LC. Therefore, a fundamental research question to be addressed is: RQ 6-In which scenarios will ad hoc distributed computing outperform delegation on the cloud?

B. Mechanisms

Authors anticipate that SNAPPs would benefit from the increase in the concentration of smartphones in proximity, from judicious and careful definition of the computing units to be processed by each smartphone and from the gains provided by the novel communication paradigms for MANETs addressed in Sec. II. Two different research lines should be investigated. The first includes mechanisms to alleviate the burden of separating computing units from the rest of the software and aggregating their results, capitalising on the recent advances in programming languages and software engineering that have started to emerge with multi-core computing. The second line consists in investigating mechanisms for speeding up computing delegation, namely by using preloaded computing blocks, in order to approximate the syntax of the work delegation to the one found in remote procedure calls, complemented with innovative distributed approaches, of which pipelining is a fitwell example. Therefore, in the scope of distributed computing, research must be able to answer the following question: RQ 7-What mechanisms should be put in place to improve the performance of ad hoc distributed computing?

V. RETHINKING MOBILE SOCIAL APPLICATIONS SNAPPs can be described as being special cases of crowdsourcing apps. Crowdsourcing captures systems that outsource tasks, data collection and aggregation to the crowd [START_REF] Doan | Crowdsourcing systems on the world-wide web[END_REF]. Examples of mainstream wired systems include YouTube, which collects and displays videos, Wikipedia, which aggregates and presents textual knowledge bases, Amazon, which outsources product reviews to customers, BitTorrent peer-to-peer file sharing or shared processing such as in SETI@home [START_REF] Anderson | Boinc: A system for public-resource computing and storage[END_REF]. These systems allow to gather huge amounts of data from a large amount of users. In order to overcome information overload, they usually offer filter mechanisms such as recommendations and profile-based personalisation. Crowdsourcing apps generally leverage on the huge amount of users that can be tapped when geographical barriers are removed and on the user's spontaneous motivation to provide content. This contrasts with SNAPPs, which have to rely on the contributions of nearby users to store and process data and where content is mainly inferred and system-generated (a system with similar assumptions for wired networks is described in [START_REF] Boutet | Whatsup: News, from, for, through, everyone[END_REF]). This poses several new challenges. Hereafter, we discuss three of them, namely challenges in business models, challenges in privacy and anonymity, and challenges in development models.

A. Business Models

SNAPPs strongly depends of its wide adoption as, to be useful, it requires a critical mass of co-located users. Building a successful business model for sharing resources is challenging, as many unsuccessful attempts illustrate. For instance an initiative that aimed at promoting hotspot sharing among neighbours failed to get enough users to gain traction. In this case, users felt that there was a lack of accountability [START_REF] Middleton | An exploration of user-generated wireless broadband infrastructures in digital cities[END_REF] and thus they did not feel comfortable to share their connection. This problem illustrates an issue that was simply not taken into account when the business model was designed. New business models will have to be investigated to capture user assumptions and provide adequate value propositions [START_REF] Osterwalder | Business Model Generation: A handbook for visionaries, game changers and challengers[END_REF] that will motivate users to adopt and use SNAPPs. These models might be based on innovative bartering schemes [START_REF] Berlanga | Ad hoc transient communities: towards fostering knowledge sharing in learning networks[END_REF], decentralised monetary systems as well as contextual reputation and trust mechanism.

This leads to the following open research question:

RQ 8-What are the characteristics of business models that encourage the adoption and usage of SNAPPs?

B. Privacy & Anonymity

Privacy was identified early on as one of the key issues related to information sharing, as exemplified by Mason's 1986 seminal paper [START_REF] Mason | Four ethical issues of the information age[END_REF]. Twenty-five years later, and despite a tremendous change in technology, the core of these concerns still applies and became especially relevant with the advent of social networking [START_REF] Parish | Papa knows best: Principles for the ethical sharing of information on social networking sites[END_REF]. With SNAPPs, privacy is especially important as data will mainly be system-generated, and user resources will be shared. They are key for ensuring the community acceptance of the model and the compliance with legislation that aims to protect users' right of protection of their personal information. According to the new European regulation about the principles relating to personal data processing, the notion of purpose and the right to oblivion are essential. Among others, these principles mention "personal data must be collected for specified, explicit and legitimate purposes and not further processed in a way incompatible with those purposes" and "data subjects should have the right that their personal data are erased and no longer processed, where the data are no longer necessary in relation to the purposes for which the data are collected [..]" [START_REF] Commission | Regulation of the european parliament and of the council on the protection of individuals with regard to the processing of personal data and on the free movement of such data (general data protection regulation)[END_REF]. Research contributions should be equally devoted to monitor, validate and seek alternatives to advances that compromise security or privacy of personal information.

Open research questions could investigate if it is possible to take advantage of the fact that decentralised distributed computing relies on devices positioned in a certain proximity at a certain time to create built-in privacy mechanisms. For instance, data could be made to exist only when a given number of devices are co-located at a given place and time. This departs from current practice where data centralisation makes it easy for someone to eavesdrop on one single entry point. Furthermore, anonymity can be a sine qua non condition in order to get users on board, especially when they are asked to share contextual information. However anonymity has some drawbacks that can lead to malicious use, resource hoarding, or spamming depending on the application scenario [START_REF] Davenport | Anonymity on the internet: why the price may be too high[END_REF]. Restricting anonymous data to a collocated group can potentially decrease the feeling of anonymity and thus reduce its side effects. We believe that such parameters of anonymity should be further investigated and might provide a balance between engagement and potential drawbacks. Furthermore, we believe that privacy can also be achieved by investigating how access to individual user data should be ephemeral whereas aggregated information can be persistent. In short, we belief the following research question should be addressed: RQ 9-What are the adequate models for privacy and anonymity to support SNAPPs in order to optimise user satisfaction?

C. Development Models

Finally, application development models should be rethought in order to involve more developers in the design of SNAPPs. New models such as the Metropolis model [START_REF]The metropolis model a new logic for development of crowdsourced systems[END_REF] can be used as starting point for a reflection. This model takes a community-driven approach where software is built in a decentralised fashion by open teams and there is little control on who contributes, using the concept of mashability, where software parts can be used and reused, and emergent behaviour, which implies that mechanisms that go beyond the vision of the originators may appear. This final point can be captured by the following research question: RQ 10-What are the characteristics of development models that motivate developers to design SNAPPs?

VI. CONCLUSION

Developing advanced social networking apps (SNAPPs) is a challenging task. We believe that it will involve dramatic paradigm shifts in the way we think about mobile distributed systems. In this position paper, we presented a research agenda that aims at providing a path towards such paradigm shifts. This agenda is expected to open novel venues both at the societal and research level. At the research level, this agenda innovates in the experimentation of three novel concepts: the possibility of mobile devices in proximity to share CPU cycles, communicate using fuzzy messages, possibly learning on the fly the communication patterns and, finally, to cooperate in the storage of the knowledge that was previously acquired. These are interesting challenges that can open new research directions on the field of the mobile ad hoc networks and ubiquitous computing. At the societal level, it is expected that the public availability of software libraries and communication standards pave the way for the viral development of a novel class of applications that can contribute for an improved quality of life of worldwide citizens.

Fig. 1 .

 1 Fig. 1. Research Streams Alignment


E Altman
email: eitan.altman@inria.fr

P Bernhard
email: pierre.bernhard@inria.fr

S Caron

G Kesidis
email: kesidis@engr.psu.edu.

J Rojas-Mora

S Wong
email: swong@udc.es

A Model of Network Neutrality with Usage-based Prices *

wrote that network neutrality "usually means that broadband service providers charge consumers only once for Internet access, do not favor one content provider over another, and do not charge content providers for sending information over broadband lines to end users." In this paper we study the implications of non-neutral behaviors under a simple model of linear demand-response to usage-based prices. We take into account advertising revenues for the content provider and consider both cooperative and non-cooperative scenarios. In particular, we model the: impact of side-payments between service and content providers, consider an access provider that offers multiple service classes, and model leader-follower (Stackelberg game) dynamics. We finally study the additional

Introduction

Network neutrality is an approach to providing network access without unfair discrimination among applications, content or traffic sources. Discrimination occurs when there are two applications, services or content providers that require the same network resources, but one is offered better quality of service (shorter delays, higher transmission capacity, etc.) than the other. How to define what is "fair" discrimination is still subject to controversy, and the underlying economic and policy issues have not been fully debated 1 . A preferential treatment of traffic is considered fair as long as the preference is left to the user 2 . Internet Service Providers 1 The recent decision on Comcast v. the FCC was expected to deal with the subject of "fair" traffic discrimination, as the FCC ordered Comcast to stop interfering with subscribers' traffic generated by peer-to-peer networking applications. The Court of Appeals for the District of Columbia Circuit was asked to review this order by Comcast, arguing not only on the necessity of managing scarce network resources, but also on the non-existent jurisdiction of the FCC over network management practices. The Court decided that the FCC did not have express statutory authority over the subject, neither demonstrated that its action was "reasonably ancillary to the [...] effective performance of its statutorily mandated responsibilities". The FCC was deemed, then, unable to sanction discriminatory practices on Internet's traffic carried out by American ISPs, and the underlying case on the "fairness" of their discriminatory practices was not even discussed. 2 Nonetheless, users are just one of many actors in the net neutrality debate, which has been enlivened throughout the world by several public consultations for new legislations on the subject. The first one, proposed in the USA, was looking for the best (ISPs) may have interest in traffic discrimination either for technological or economic purposes. Traffic congestion, especially due to high-volume peer-to-peer traffic, has been a central argument for ISPs against the enforcement of net neutrality principles. However, it seems many ISPs have blocked or throttled such traffic even during periods without congestion.

ISPs recently claimed that net neutrality acts as a disincentive for capacity expansion of their networks. In [START_REF] Cheng | The debate on net neutrality: A policy perspective[END_REF], the authors studied the validity of this argument and came to the conclusion that, under net neutrality, ISPs invest to reach a social optimal level, while they tend to under/over-invest when neutrality is dropped. In their setting, ISPs stand as winners while content providers (CPs) are left in a worse position, and users who pay the ISPs for preferential treatment are better off while other consumers have a significantly worse service.

ISPs often justify charging CPs by quantifying the large amount of network resources "big" content providers use. On the other hand, the content and services the CPs offer contribute to the demand for Internet access, and thus benefit the ISPs. Shapley values may be used to obtain fair and Pareto optimal revenue-sharing between different types of players, e.g., [START_REF] Ma | Interconnecting eyeballs to content: A Shapley value perspective on ISP peering and settlement[END_REF][START_REF] Ma | On cooperative settlement between content, transit and eyeball internet service providers[END_REF]. That is, Shapley values can prescribe whether and how (i) CPs should share third-party advertising revenue enabled by subscribers' network access, or (ii) ISPs should share subscription revenue enabled by their customers' demand for online content and services.

In this paper, we focus on violations of the neutrality principles defined in [START_REF] Hahn | The Economics of Net Neutrality[END_REF] where broadband service providers charge consumers more than "only once" through usage-based pricing, and charge content providers through side-payments.

Within a simple game-theoretic model, we examine how regulated 3 side payments, in either direction, and demand-dependent advertising revenues affect equilibrium usage-based prices. We also address equilibria in Stackelberg leader-follower dynamics.

means of preserving a free and open Internet [15]. The second one, carried out in France, asks for different points of view over net neutrality [START_REF]Consultation publique sur la neutralité du net[END_REF]. A third one was presented by the EU during summer 2010, looking for a balance on the parties concerned as users are entitled to access the services they want, while ISPs and CPs should have the right incentives and opportunities to keep investing, competing and innovating [START_REF]Neelie Kroes, Vice-President of the European Commission, Commissioner for the Digital Agenda[END_REF]. 3 In the European Union, dominating positions in telecommunications markets (such as an ISP imposing side-payments to CPs at a price of his choice) are controlled by the article 14, paragraph 3 of the Directive 2009/140/EC, considering the application of remedies to prevent the leverage of a large market power over a secondary market closely related.

The rest of the paper is organized as follows. In section 2, we describe a basic model and derive Nash equilibria for competitive scenarios and optimal collaborative scenarios. We consider potentially non-neutral side-payments in section 3 and advertising revenues in section 4, analyzing in each case how they impact equilibrium revenues. We consider an ISP offering multiple service classes in section 5. In section 6, we study leader-follower dynamics. In Section 7 we consider the case where one provider can control the amoount of side payments from the other one. We show that this results in a dramatic degradation of performance for all actors: at equilibrium, the demand is shown to be zero. We conclude in section 8 and discuss future work.

Basic model

Our model encompasses three actors:

the internauts (users), collectively, a network access provider for the internauts, collectively called ISP1, and a content provider and its ISP, collectively called CP2.

The two providers play a game to settle on their (usagebased) prices. The internauts are modeled through their demand response. Consumers are assumed willing to pay a usage-based fee (which can be $0/byte) for service/content that requires both providers.

Denote by p i ≥ 0 the usage-based price leveed by provider i (ISP1 being i = 1 and CP2 being i = 2). We assume that the demand-response of customers, which corresponds to the amount (in bytes) of content/bandwidth they are ready to consume given prices p 1 and p 2 , follows a simple linear model (e.g., [START_REF] Economides | Net Neutrality: Non-Discrimination and Digital Distribution of Content Through the Internet[END_REF]):

D = D 0 -d(p 1 + p 2 ). (1)
With such a profile, we are dealing with a set of homogeneous users sharing the same response coefficient d to price variations. Infrastructure and operating costs borne by the ISPs and CPs [START_REF] Musacchio | A two-sided market analysis of provider investment incentives with an application to the net-neutrality issue[END_REF] are not considered here.

The parameter D 0 corresponds to the demand under pure flat-rate pricing (p 1 = 0 = p 2 ). Demand should be non-negative, i.e.,

p 1 + p 2 ≤ D 0 d =: p max .
Provider i's usage-based revenue is given by

U i = Dp i . (2)

Non-Cooperation

Suppose the providers do not cooperate. An interior Nash Equilibrium Point (NEP) (p * 1 , p * 2 ) of this twoplayer can be obtained from the first order optimality conditions

∂U i ∂p i (p * 1 , p * 2 ) = 0, for i = 1, 2, which lead to p * 1 = p * 2 = D 0 /(3d)
. The demand at equilibrium is thus D * = D 0 /3 and the revenue of each provider is

U * i = D 2 0 9d . ( 3
)

Collaboration

Now suppose there is a coalition between ISP1 and CP2. Their overall utility is then

U total := U 1 +U 2 = Dp, and an optimal point (p * 1 , p * 2 ) satisfies ∂U total ∂p i (p * 1 , p * 2 ) = D * -d(p * 1 + p * 2 ) = 0 for i = 1, 2, which yields p * := p * 1 + p * 2 = D 0 /(2d).
The demand at equilibrium is then D * = D 0 /2, greater than in the noncooperative setting. The overall utility U * total = D 2 0 /(4d) is also greater than D 2 0 /(4.5d) for the competitive case. Assuming both players share this revenue equally (trivially, the Shapley values are {1/2, 1/2} in this case), the utility per player becomes

U * i = D 2 0 8d , ( 4
)
which is greater than in the competitive case. So, both players benefit from this coalition.

Side-Payments under Non-Cooperation

Let us suppose now that there are side payments between ISP1 and CP2 at (usage-based) price p s . The revenues of the providers become:

U 1 = D (p 1 + p s ) ( 5 )
U 2 = D (p 2 -p s ) ( 6 )
Note that p s can be positive (ISP1 charges CP2 for "transit" costs) or negative (CP2 charges ISP1, e.g., for copyright remuneration4 ). It is expected that p s is not a decision variable of the players, since their utilities are monotonic in p s and the player without control would likely set (usage-priced) demand to zero to avoid negative utility. That is, p s would normally be regulated and we will consider it as a fixed parameter in the following (with |p s | ≤ p max ). First, if |p s | ≤ 1 3 p max , the equilibrium prices are given by

p * 1 = 1 3 p max -p s p * 2 = 1 3 p max + p s but demand D * = D 0 /3 and utilities U * i = D 2 0
9d are exactly the same as (3) in the competitive setting with no side payment. Therefore, though setting p s > 0 at first seems to favor ISP1 over CP2, it turns out to have no effect on equilibrium revenues for both providers.

Alternatively, if p s ≥ 1 3 p max , a boundary Nash equilibrium is reached when p * 1 = 0 and p * 2 = 1 2 (p max + p s ), which means ISP1 does not charge usage-based fees to its consumers. Demand becomes D * = 1 2 (D 0dp s ), and utilities are

U * 1 = (D 0 -dp s )dp s 2d U * 2 = (D 0 -dp s ) 2 4d Though p * 1 = 0, U *
1 is still strictly positive, with revenues for ISP1 coming from side-payments (and possibly from flat-rate monthly fees as well). Furthermore,

p s ≥ 1 3 p max ⇔ dp s ≥ 1 2 (D 0 -dp s ), which means U * 1 ≥ U *
2 : in this setting, ISP1's best move is to set his usagebased price to zero (to increase demand), while he is sure to achieve better revenue than CP2 through sidepayments.

Finally, if p s < -1 3 p max , the situation is similar to the previous case (with -p s instead of p s ). So, here p * 2 = 0 and p * 1 = 1 2 (p maxp s ), leading to U * 2 ≥ U * 1 . To remind, herein revenues U i are assumed usagebased, which means there could also be flat-rate charges in play to generate revenue for either party. Studies of flat-rate compare to usage-based pricing schemes can be found in the literature, see, e.g., [START_REF] Kesidis | On Flat-Rate and Usagebased Pricing for Tiered Commodity Internet Services[END_REF].

Advertising revenues

We suppose now that CP2 has an additional source of (usage-based) revenue from advertising that amounts to Dp a . Here p a is not a decision variable but a fixed parameter. 5

Non-Cooperation

The utilities for ISP1 and CP2 are now:

U 1 = [D 0 -d • (p 1 + p 2 )] (p 1 + p s ) ( 7 )
U 2 = [D 0 -d • (p 1 + p 2 )] (p 2 -p s + p a ) ( 8 )
Here, the Nash equilibrium prices are:

p * 1 = 1 3 p max -p s + 1 3 p a p * 2 = 1 3 p max + p s - 2 3 p a
The cost to users is thus p * = 2 3 p max -1 3 p a while demand is D * = 1 3 (D 0 + dp a ). Nash equilibrium utilities are given by

U * i = (D 0 + dp a ) 2 9d for i = 1, 2, (9)
which generalizes equation ( 3) and shows how advertising revenue quadratically raises players' utilities.

Collaboration

The overall income for cooperating providers is

U total = (D 0 -dp)(p + p a ). (10)
So, solving the associated first-order optimality equation yields

p * = p max -p a 2 . ( 11
)
The optimal demand is then D * = (D 0 + dp a )/2, and the maximal total revenue is U * total = (D 0 + dp a ) 2 /(4d). Assuming this revenue is split equally between the two providers, we get for each provider the equilibrium utility

U * i = (D 0 + dp a ) 2 8d , ( 12
)
which generalizes equation ( 4). As before, providers and users are better off when they cooperate. Thus, we see that p a > 0 leads to lower prices, increased demand and more revenue for both providers (i.e., including ISP1).

ISP Providing Multiple Service Classes

In this section, we suppose ISP1 is offering two types of network access service: a low-quality one l at price p l , and a high-quality one h at price p h ≥ p l . The role of multiple service classes in a neutral network, i.e., as selected by the users, has previously been explored, e.g., [START_REF] Kesidis | Congestion control alternatives for residential broadband access by CMTS[END_REF] 6 . Here, we split the demand D into D l and D h : D = D l + D h (we will describe later how we implement the dichotomy between D l and D h ). For now, assume the overall demand still has a linear response profile, i.e.,

D = D 0 -d( p l + p h formerly p1 +p 2 ). ( 13
)
First, we make reasonable assumptions on D l :

1. Pricing incentives: Define Δp := p hp l . Δp is an incentive for consumers to chose between classes l and h: the higher Δp is, the more likely users are to select l. Thus, if we take x := 1/Δp and y := D l /D, we may see y as a function of x and model this pricing response with the following properties:

y (x) ≤ 0 (D l increases with Δp) ( 14
)
y(0) = 1 (D l ↑ D as Δp ↑ ∞) (15) y(∞) = 0 (D l ↓ 0 as Δp ↓ 0) (16)
2. Congestion incentives: As D l approaches D, we assume congestion occurs in the low-quality network, further deterring users to chose it. This motivates the additional assumption that

|y (x)| ↓ 0 as x ↓ 0, (17)
that is, D l decelerates as it gets closer to D.

Define

δ := Δp γp max , ( 18
)
where γ > 0 is an additional users' price-sensitivity parameter. The following demand relation satisfies all conditions ( 14), ( 15), ( 16) and ( 17):

D l := 1 -e -δ D. ( 19
)
The providers' utilities are then:

U 1 = D l p l + D h p h = D p l + Δpe -δ (20) U 2 = Dp 2 (21)

Collaboration

If both players cooperate, their overall utility is

U total = D p 2 + p l + Δpe -δ .
There is no NEP with strictly positive prices p i ≥ 0 for i = 1, 2. To specify the boundary NEP (where at least one usage-based price is zero), define

φ(x) := (1 -x)e -x
and note that φ is a bijection of [0, 1].

-If p 2 = 0, NEP conditions imply

δ * = φ -1 (1/2) p * l = 1 3 1 2 -γδe -δ p max
Utility at the NEP is therefore

U * total = D 2 0 9d 1 2 + 2γδe -δ . 2 + 2e -δ -3 δγ (22)
In this setting, the value of U total is upper bounded by ≈ 0.162

D 2 0
d which is achieved when γ ≈ 1.53 (recall that γ is not a decision variable).

-If p l = 0, then p h = 0 and p 2 = 1 2 p max , yielding

U total = D 2 0 4d . ( 23
)
Hence, irrespective of consumers' sensitivity γ to the price gap Δp, the best solution for the coalition is to set-up usage-based pricing for content only, at price p 2 = p max /2, while network access is subject to flatrate pricing (p l = p h = 0).

Splitting Demand-Response Coefficient

Now consider splitting the demand-response coefficient d into d l , d h and d 2 , that is:

D = D 0 -d l p l -d h p h -d 2 p 2 . ( 24
)
If

d 2 = d l + d h , ( 25
)
then the interior equilibrium conditions ∇U total = 0 yield:

δ = φ -1 (d h /d 2 ) p l + p 2 = D 0 2d 2 - δΔp 0 2 d h d 2 + e -δ
When the demand-response coefficients satisfy (25), we have an equilibrium line. Vector field plots of U total suggest it is attractive (see Figure 5.2). In this particular setting, providers can thus reach U * total with non-flat rate pricing.

However, if d 2 = d l +d h , there exists a line of attraction, but with a non-null gradient on it driving players toward border equilibria. Hence, the conclusion of subsection 5.1 also holds in this more generalized setting.

Non-Cooperation

When ISP1 and CP2 compete, again there is no interior NEP (with all prices p i strictly positive). In fact, the condition ∇ p l ,p h U 1 = 0 implies p l = 0 = p h and D = 0, so ISP1 has to relax condition ∂U1 ∂p l = 0 by setting p l = 0 (i.e., flat-rate pricing for the best-effort service l). The solution to the two remaining Nash equilibrium conditions is then:

p 2 = 1 4 9γ 2 + 2γ + 1 -3γ + 1 • p max (26)
p h = γ 2 9γ 2 + 2γ + 1 -3γ + 2 • p max (27)
By defining f 2 (γ) := p 2 /p max and f h (γ) := p h /p max , we then have 2 shows utilities at equilibrium (as fractions of D 0 p max ). We see that, in any case, CP2 has the advantage in this game: U * 2 is always greater to U * 1 , irrespective of consumers' sensitivity γ to usage-based prices.

U * 1 (γ) = f h (γ) • (1 -f h (γ) -f 2 (γ))D 0 p max U * 2 (γ) = f 2 (γ) • (1 -f h (γ) -f 2 (γ))D 0 p max Figure
Here, γ → 0 means users are so sensitive to any usage-based price that they will always choose the besteffort service (which is subject to flat-rate pricing). Users' price sensitivity decreases as γ increases, with the limit γ → ∞ corresponding to the setting of section 2 with

lim γ→∞ U * i (γ) = D 2 0 9d .

Stackelberg equilibrium

Stackelberg equilibrium corresponds to asymmetric game in which one player is the leader and the other a followers. That is, actions are no longer taken independently: the leader takes action first, and then the follower reacts. Though the dynamics of the games are different from the previous study, equations [START_REF] Hahn | The Economics of Net Neutrality[END_REF] Therefore, when ISP1 is the leader, at the NEP demand is D * = 1 4 (D 0 + dp a ) and utilities are:

U * 1 = 1 8d (D 0 + dp a ) 2 , ( 28
)
U * 2 = 1 16d (D 0 + dp a ) 2 . ( 29
)
Suppose now that CP2 is the leader and sets p 2 first. Similarly, we find:

p * 2 = 1 2 p max + p s - 1 2 p a p * 1 = 1 4 p max -p s + 1 4 p a
These values yield the same cost p * and demand D * for the internauts at the NEP, while providers' utilities become:

U * 1 = 1 16d (D 0 + dp a ) 2 , ( 30
)
U * 2 = 1 8d (D 0 + dp a ) 2 . ( 31
)
Therefore, in either case of leader-follower dynamics, the leader obtains twice the utility of the follower at the NEP (yet, his revenue is not better than in the collaborative case).

Further abandoning neutrality

Throughout we assumed that the side payments between service and content providers were regulated. If p s is allowed to be determined unilaterally by the service provider or by the content provider (as part of the game described in Section 3 or 4), then the worst possible performance is obtained at equilibrium. More precisely, the demand at equilibrium is zero, see [START_REF] Altman | A study of non-neutral networks[END_REF]. The basic reason is that if the demand at equilibrium were not zero then a unilateral deviation of the provider that controls the side payment results in a strict improvement of its utility. (Note that the total demand is unchanged as it does not depend on p s .) More generally, assume that an ISP is given the authority to control p s and that its utility can be expressed as U = f (D) × (g(p s ) + h) where f is any function of the demand (and possibly also of prices other than p s ), g is a monotone strictly increasing function of p s , and h does not depend on p s . Then at equilibrium, necessarily f (D) = 0, otherwize U can be further increased by the provider by (unilaterally) increasing p s .

The same phenomenon holds also in case the CP is given full control over p s .

Conclusions and on-going work

Using a simple model of linearly diminishing consumer demand as a function of usage-based price, we studied a game between a monopolistic ISP and a CP under a variety of scenarios including consideration of: non-neutral two-sided transit pricing (either CP2 participating in network costs or ISP1 paying for copyright remuneration), advertising revenue, cooperation and leadership.

In a basic model without side-payments and advertising revenues, both providers achieve the same utility at equilibrium, and all actors are better off when they cooperate (higher demand and providers' utility).

When regulated, usage-based side-payments p s come into play, the outcome depends on the value of |p s | compared to the maximum usage-based price p max consumers can tolerate: when |p s | ≤ 1 3 p max , providers shift their prices to fall back to the demand of the competitive setting with no side-payments; when |p s | ≥ 1 3 p max , the provider receiving side payments sets its usage-based price to zero to increase demand, while it is sure to be better off than his opponent.

When advertising revenues to the CP come into play, they increase the utilities of both providers by reducing the overall usage-based price applied to the users. ISP1 and CP2 still share the same utility at equilibrium, and the increase in revenue due to advertising is quadratic.

We considered in section 5 the implications of service differentiation from the ISP. In our model, when ISP1 and CP2 cooperate, the best solution for them is to set-up usage-based prices for content only and flatrate pricing for network access. However, when providers do not cooperate, the ISP optimally offers its best-effort service for a flat rate (zero usage-based cost), resulting in more usage-based revenue for the CP.

Under leader-follower dynamics, the leader obtains twice the utility of his follower at equilibrium; yet, he does not achieve a better revenue than in the cooperative scenario.

In subsequent work [START_REF] Caron | Application Neutrality and a Paradox of Side Payments[END_REF], we explored the effects of content-specific (i.e., not application neutral) pricing, including multiple CPs providing different types of content. Also, we considered competition among multiple providers of the same type, including different models consumer stickiness (interia or loyalty). In on-going work, we are also considering providers' infrastructure and operating costs (as in, e.g., [START_REF] Musacchio | A two-sided market analysis of provider investment incentives with an application to the net-neutrality issue[END_REF]), more complex models of end-user demand and their collective social welfare, and the effects of different options for flat-rate pricing (e.g., [START_REF] Odlyzko | Internet pricing and history of communications[END_REF][START_REF] Kesidis | On Flat-Rate and Usagebased Pricing for Tiered Commodity Internet Services[END_REF]).

Fig. 1

 1 Fig. 1 Attraction of the equilibrium line.

Fig. 2

 2 Fig. 2 Utilities as functions of users' sensitivity to usage-based pricing.

  and (8) still hold, with fixed p a ≥ 0 and regulated p s . In the following, we need to assume that + p max + p sp a ).

	p s ≤	1 2	p max +	1 2	p a
	p a ≤	1 3	p max +	1 4	p s
	so that NEPs are reachable with positive prices.
	If ISP1 sets p 1 , then CP2's optimal move is to set
	p 2 = (-p 1 This expression yields D = d 1 2 2 (p max -p 1 -p s + p a ) and U 1 = d 2 (p max -p 1 -p s +p a )(p 1 +p s ). Anticipating CP2's
	reaction in trying to optimize U 1 , the best move for
	ISP1 is thus to set
	p * 1 =		1 2	p max -p s +	1 2	p a ,
	which yields
	p * 2 =	1 4	p max + p s -	3 4	p a .

In France, a new law has been proposed recently to allow download of unauthorized copyright content, and in return be charged proportionally to the volume of the download.

One may see pa as the result of an independent game between CP2 and his advertising sources, the details of which are out of the scope of this paper.

Non-neutral class assignment to applications, i.e., not application-neutral networking, is discussed in[START_REF]Network Neutrality[END_REF].

Acknowledgements We thank the anonymous reviewers for their helpful feedback. The work by Penn State is supported in part by the National Science Foundation under grant 0916179 and by a Cisco Systems URP gift.