A fair cooperative content-sharing service

Computer Networks 57 (2013) 1955–1973

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Computer Networks

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A fair cooperative content-sharing service

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⇑ Corresponding author. Address: University Mediterranea of ReggioCalabria, DIIES Department, 89100 Reggio Calabria, Italy. Tel./fax: +390965 875276.

E-mail addresses: [email protected] (L. Militano), [email protected] (A. Iera), [email protected] (F. Scarcello).

L. Militano a,⇑, A. Iera a, F. Scarcello b

a University Mediterranea of Reggio Calabria, DIIES Department, Italyb University della Calabria, Cosenza, DIMES Department, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 31 July 2012Received in revised form 31 January 2013Accepted 22 March 2013Available online 8 April 2013

Keywords:Wireless cooperationFairnessContent sharingNucleolusGame TheoryMediated P2P process

Wireless cooperative content sharing, based on the synergistic use of cellular and short-range technologies, has recently gained much interest from academic and industrial com-munities. Besides energy saving and information transfer delay reduction, this paradigmcan enable a significant reduction in cellular bandwidth usage, which also means monetarysaving for users. In fact, such a cooperation is usually opposed by network and service pro-viders, because it strongly reduces their potential profits. This paper deals with the pro-vider perspective, too. In particular, a ‘‘mediated cooperative behavior’’ is proposed andanalyzed within a scenario of short-range wireless file-sharing. The basic idea is that pro-viders offer the possibility to users of cooperatively downloading contents, and increasetheir own profits because more users are attracted by such a service. Indeed, by participat-ing in the devised service, users both avoid a (possibly expensive) stand-alone download ofthe desired product, and benefit of a special group-discount. The costs (and downloadtasks) distribution among users is based on a cooperative game theoretic model. Indeed,suitable solution concepts are applied to provide a fair solution, acceptable by all users,and hence to overcome the limitation of traditional optimization approaches to costs(and tasks) distribution.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Cooperation over short-range links among cellular de-vices is a paradigm, which has recently gained wide inter-est in the research community [1]. According to it, groupsof users interested in a common content and in proximityto each other, might cluster together and exchange, overcost-free, energy efficient, and fast short-range links, a con-tent downloaded through the costly cellular link. Advanta-ges from the end-user point of view, in terms of energyefficiency, throughput enhancement, and cost reduction, arequite evident [2].

However, we are also interested in the network and ser-vice provider perspectives, describing a framework where

providers may have economic benefits, too. The wirelesscooperation paradigm is conceptually very close to classicP2P and file sharing services, which show similar issuesstill requiring a solution. P2P file sharing services are now-adays highly successful among the younger generationsand it is a common practice to share multimedia contentsuch as music, videos, images, e-books, or similar, throughP2P platforms to minimize the monetary cost of thecontent.

Of course, whenever any form of content sharing vio-lates copyright constraints, this behavior may cause largeprofit losses to content and network providers. The mainreason that moves the end-user to go the way of illegalityis the monetary service price, which is often judged to betoo high. Network and service providers seem to be unableto find solutions to stop this phenomenon. In the authors’opinion, a successful reaction for providers is to promotethemselves as an active part of the system, by offeringwhat we call a ‘‘mediated cooperative framework for file

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1956 L. Militano et al. / Computer Networks 57 (2013) 1955–1973

sharing service’’. The idea is that users in a group will beable to select a special P2P-option when they buy someproduct. This way, they get a group license that benefitsof a high discount with respect to standard single-user li-censes, and they are allowed to freely share the productwithin the P2P wireless network of the group. Moreover,users download only some parts of the whole product overthe costly phone-link. Indeed, the service coordinator willcompute and assign to users the fractions of the productto be downloaded by each of them, by taking into accountdownload costs, time and the energy consumption.

The main advantage for providers would derive fromthe increased chances to involve in the business thosenodes (the majority) inherently oriented to ‘‘legality’’, butthat avoid to access the provider downloading-service be-cause prices are too high (at least with respect to their ac-tual interest in that product). Indeed, in the proposedframework, users may save money because of the specialgroup discount, so that the actual price to be paid couldmatch the actual value/interest they assign to the product.Moreover, they have further pros in terms of energy/throughput/download cost, as well as the additional secu-rity factor guaranteed by a downloading-service under thedirect control of providers (instead of possible illegal anduncontrolled alternatives).

Surely, to make this ‘‘mediated wireless cooperation’’mechanism work properly, a key feature that the providershall promote, to catch the interest of more users, is theimplementation of a cost distribution among cooperatingnodes, which is judged fair by all the players. This featuremay be the only effective incentive to access the servicesince, in real environments, where nodes are rational andselfish players, it is difficult to reach such an agreementin cooperation. In particular, any proposed cost allocationshould also be tested according to the stability property,guaranteeing that no (sub)group of users has an incentiveto leave the cooperation group and to form a differentcoalition.

Traditional optimization techniques show their limits inguaranteeing these requirement for all the participatingmembers. Indeed, they only deal with the minimizationof some global measure (total cost, energy, time, etc.),but provide no indication on how to divide such an optimalvalue among nodes while considering their individual orjoint contribution to the mechanism. Therefore, the frame-work should consider solutions that guarantee fairness andstability in the cost distribution allowing the selection ofthe best suited coalition partition for the interested users.This way, the fare to be paid by each player (member ofthe group) takes into account his contribution to any pos-sible coalition in terms of download costs of his terminalover the cellular link, possible agreements with the pro-vider (e.g., frequent buyers), and so on. In particular, theservice coordinator will act as an ‘‘impartial’’ entity guar-anteeing that only solutions are applied that are judgedfair, according to the proposed (publicly available) crite-rion. Moreover, since every player contributes to the pro-cess (at least allowing the group to obtain a highermultiple-license discount), the mechanism also avoids freeriding, a typical behavior of pure peer-to-peer systems

where some nodes get benefits from the community with-out giving anything back.

Based on the above considerations the main objectivesof this paper are: (i) to propose a framework that gives avalid alternative to classic P2P systems, allowing the ser-vice providers to participate in the cooperation processand benefit from it as well; (ii) to include in the frameworksome proposals that guarantee fairness and stability in thecost distribution as an alternative to traditional optimiza-tion techniques; (iii) to model and analyze well-knownsolution concepts from cooperative Game Theory, to guar-antee fairness in the cost distribution for the specific prob-lem; and (iv) to perform an analysis on the monetarysavings and profits for the involved entities under systemand user constraints related to personal and technologicalparameters.

The rest of this paper is structured as follows. Next sec-tion gives an overview of related work relevant to core is-sues and techniques under investigation in this research. Adetailed description of the reference cooperative file shar-ing service, the user cost minimization step, and the gametheoretic model for the problem are given in Section 3. Athorough performance evaluation is presented in Section 4,while final remarks are given in the conclusion section.

2. Related works

From the literature, several research contributions areavailable, which propose improvements in the perfor-mance of remote content downloads [3]. Solutions are,for instance, based on bandwidth aggregation of multipleinterfaces belonging to either the same device [4] or to dif-ferent nearby devices [5]. Interesting contributions also ad-dress modeling and evaluation issues relevant tocommunication architectures that exploit the synergy be-tween cellular and short-range systems. As an example,[6,7] show how cellular and short-range networks (WLAN,Ad hoc, and MANET) can be integrated to improve the per-formance levels. In [8] the attention has been given to theenergy consumption and transfer delay benefits obtainablethrough this communication architecture. In contrast, is-sues such as end-user cost reduction due to bandwidthoccupation decrease and network/content provider profitlosses have attracted a little attention up to now. The focusof the present paper is to cover this lacking aspect, tryingto introduce a service model able to attract the interestof network/content providers for the wireless cooperativecontent sharing. This is actually of utmost importance forthe success of the framework. Cooperation over short-range links and classic P2P show similar problems fromthe economics point of view for the network/content pro-vider; thus, it is worth recalling P2P related researchesabout this issue to better highlight the differences amongthem.

From the moment the first file sharing services ap-peared on the market, the providers started analyzinghow to deal with such services [9], and considering eitherto cooperate with or to fight against them. There is muchongoing research activity trying to understand socio-eco-nomic aspects associated to file sharing services, like for

L. Militano et al. / Computer Networks 57 (2013) 1955–1973 1957

BitTorrent in [10]. Moreover, in proposing content distri-bution services, counteractions to fight against unautho-rized illegal content publishers represent an importantpart of the service model [11]. As claimed in [12], distribu-tion cost is a key reason that prevents the content provid-ers from making great amounts of content available fordownload in P2P content distribution networks. Further-more, [12] points out that in classic P2P systems costsare pushed from the content distribution networks to theInternet Service Providers (ISPs). On the other hand, inwireless systems, user cooperation over ‘‘private’’ shortrange links reduces the overall income for the ISP.

The framework considered in the present paper, in-stead, looks at the provider as a ‘‘promoter’’ or ‘‘mediator’’of a P2P-like file sharing service, which controls and coor-dinates the service and, in doing so, obtains some benefitsfor itself. A way to reach this objective is to promote highlyattractive (but monitored) cost reductions for users whocooperatively download some contents. On the other hand,a suitable game theoretic formulation allows us to achievethis goal while taking care of fairness and stability aspects,too.

Game Theory is an analytical framework that attemptsto analyze the behavior of rational entities with theirown interests in reciprocal interactions [13]. Recently ithas been applied also to various research fields relevantto wired and wireless communication networks [14].Among cooperative game based contributions, the so-called coalitional problems are gaining large interest withinthe research community [15]. In [16] the focus is on vehic-ular networks, in [17] a coalitional problem is proposed tostudy fairness and cooperation gains in virtual MIMO sys-tems, in [18] packet forwarding issues in ad hoc networksare addressed, while in [19] a task allocation problem isstudied in a software system. Game theoretic models havebeen also applied to pricing schemes in cognitive wirelessnetworks [20] or in heterogeneous wireless networks[21,22]. In a different study [23], the authors of the presentpaper also showed how cooperative Game Theory can beapplied to provide a fair energy consumption cost-distribu-tion in a cooperative cluster in which the introduced com-munication-systems constraints play a significant role.Moreover, a recent interesting contribution exploits GameTheoretical notions to deal with fairness in peer-assistedservices for content delivery networks (for live streamingand similar highly resource-demanding contents) [24]. In-deed, such networks would benefit from a peer-to-peerarchitecture to reduce their operating costs, and theauthors study a fluid Shapley value approach to provide asuitable incentive scheme for users cooperating in the con-tent distribution process.

P2P systems are often studied through non-cooperativegame theoretic models to introduce incentives or to coor-dinate the system (for example [25] and [26]). The medi-ated service framework proposed in this paper is notself-organizing because it is controlled by the provider.At the same time, the users do not need any incentive tocooperate. Indeed, nodes are naturally incentivized tocooperate by the immediate monetary savings they experi-ence, where the larger is the coalition (group) the larger isthe discount (controlled by the provider). In fact, the mon-

etary based economic-model is a point of strength of thecooperative process proposed in this paper, and coopera-tive Game Theory is the most natural framework to studyagreements and interactions among such involved entities.

3. The cooperative file sharing framework

With reference to the service framework introduced inSection 1, assume there is a content provider P that offersthe P2P group-option to its clients, and plays the role ofthe Cooperation Server plotted in Fig. 1. In order to reachits goal of selling licenses of its product to all interestedusers (also, nodes), the service coordinator implements apolicy aiming at minimizing the overall monetary cost forthe users, while allowing a cost distribution that is per-ceived to be a fair and stable one. These are the compulsoryconditions for the wireless cooperative process to be ac-cepted by all parties. Actually no unique definition can begiven for what a fair solution is, but several solution con-cepts have been proposed over the years in the field ofGame Theory [27]. In this paper, we shall focus on twowell-known and studied solution concepts; however, mostof the paper is actually independent of the specific chosennotion.

Let N be a group of users interested in downloadingsome product from this provider. Nodes start the proce-dure by contacting the Cooperation Server P and requestingthe desired product with the P2P option. Each node sendsinformation about its device interface identifier, cellularlink throughput, cost per second of the cellular link (oralternatively the cost per unit of data), information relatedto the short-range link they cooperate through (e.g. Blue-tooth or WLAN link). For every node i, the Server P knowsthe monetary cost cdi afforded to download the full prod-uct file from the provider, as well as the time ti requiredto complete such a download. Presenting a detailed cellu-lar model is not among the objectives of the paper. Differ-ently the aim is to analyze the impact the bandwidth costshave on the cooperative solutions. Therefore, in our perfor-mance evaluation study, we considered a wide set of cellu-lar throughput values to assess how the cooperativescenarios are influenced by this parameter. Users may alsospecify some constraints over their contribution to the pro-posed P2P framework: any user i may impose a limit on theamount of data to be downloaded in the P2P application,expressed as a fraction 0 6 DownloadBoundi 6 1 of the de-sired product file, which of course entails a bound Down-loadBoundi � cdi for the maximum download cost forplayer i. While the short-link technology is available forfree to all users in N, we consider the energy consumptionand the content transfer delay as further parameters ofinterest in the final product-sharing phase over this inex-pensive link. In particular, any user i may define a TimeCon-strainti P 0 to express the maximum time it is willing tospend to receive the wished content, in relation to thenon-cooperative download. Similarly, any user i may de-fine an EnergyConstrainti P 0 to express the maximum en-ergy it is willing to spend, compared to the non-cooperative download. In order to evaluate these con-straints, the Cooperation Server P should be able to estimate

Fig. 1. Wireless cooperative scenario.


the time and the energy consumption for the cooperativecontent download for every node. This requirement canbe fulfilled providing the service provider with a specificmodel which deals both with the short-range link andthe cellular data-exchange, as defined in Section 3.4.

A suitable pricing function p(S) is defined by P for everynon-empty group of users S # N, which may take into ac-count frequent buyers, clients with high-feedbacks, and soon. To model the intended business strategy where largegroups (buying many licenses) should be attracted, sucha pricing function is required to be sub-additive, that is,p(S [ T) 6 p(S) + p(T), for every pairs of non-intersectingsubgroups S and T. Therefore, adding users to any group al-ways leads to a lower price-per-license, so that largergroups have higher discounts, as expected.

After collecting information from nodes willing to coop-erate, the Cooperation Server reports decisions to themabout ‘‘how’’ to cooperate. This task consists in definingthe cooperative coalitions and assigning the portion ai ofcontent (file-share) that any node i in the cooperativeframework shall download over its costly cellular link,and the total cost xi for player i to get the desired product.Note that this cost includes the network cost, and thusplayer i actually pays to the content provider xi � ai � cdi.Nodes will then proceed to download their assigned file-share, and then they exchange these parts of the file overthe (free) short-range link. In general, more copies of thefile may be downloaded by nodes of the group, the onlyconstraint is that the fractions downloaded by peers coverat least a whole copy of the desired file. That is,

Pi2Nai P 1

must hold, i.e. non-overlapping file fractions (may) sum tomore than 1.

Noteworthy, because of the group-discount modeled bythe pricing function and the optimization performed to re-duce the download cost (exploiting devices with lowerbandwidth costs), the cost assigned to each node i will al-ways be not higher than the cost that i would sustain for astand-alone download (which is the sum of the content li-cense cost p({i}) and the download cost cdi). In fact, the

precise cost is determined according to a game theoreticalsolution-concept, described in the subsequent section, thatguarantees a fair cost allocation for all nodes and that is thekey issue for the success of the proposed paradigm. In par-ticular, the service coordinator needs to take into carefulconsideration the contribution of every node i in terms ofprice reduction and of device capability (bandwidth cost),to suitably evaluate how much discount it deserves.

Note that, so far, we just considered a service providerthat offers a file download service and directly partakesin a sort of ‘‘mediated’’ wireless cooperative data-exchangebased on short-range links. We have not yet considered thepossible role of the network provider (if it is distinct), thatcould oppose the proposed framework because it may re-duce its profits on the costly cellular link. In a simple ap-proach, one may just assume that the network providerhas a mutual business agreement with the service providerthat covers somehow such a loss. In fact, if the networkprovider has some control power over the proposed proto-col, we could imagine that, in the business agreement, thenetwork provider may require a lower bound on its profitper transaction, with respect to the case of stand-alonedownloads for all users. Formally, we consider in theframework an additional parameter 0 6 GainCon-straint 6 1, used to impose the constraintP

i2Nai � cdi PP

i2Ncdi � GainConstraint over the total down-load-cost of the group. We believe that even low values ofthe profit-gain constraint are reasonable: if this situation iscontrasted with typical P2P networks, where the networkprovider has no control at all, only a few users participatein the costly download phase, and thus it always suffershigh profit losses.

3.1. Game-theory solution concepts for the P2P framework

In this section, we recall the notions of Game Theoryused in this paper, mapping their meaning to the referenceproblem and highlighting how they help towards our finalobjective. For more information on this subject, the reader


is referred, e.g., to the book on Game Theory by Osborne[13].

It is natural to model the process of assigning a cost toeach cooperating player (node) in a fair way as a coalitionalcost-game G = hN,Ci with transferable utilities (TU), whereN is the set of players and C : 2N ! R is a characteristic costfunction that models the feasible cost for every coalition(set of players/nodes) S # N.

In our case, the cost function models the fact that everycoalition S has at its disposal the ability of each player i 2 Sto download the file with some costs and some constraints,besides his contribution to determine the price p(S) of thedesired product. For instance, player i may be a frequentbuyer, and its presence in S may allow the coalition toget a higher discount. Of course, this may also happen forsubgroups of players, so that some family S0 may attainsome special price, and thus S0 # S entails that p(S) willbe particularly cheap. Therefore, a fair price assignmentshould consider all possible contribution of players, tryingto make everyone happy, and not only to meet the imposedconstraints.

Henceforth, components of any vector x 2 RjNj are one-to-one associated with players in N, so that xi denotes thecomponent associated with player i 2 N. Moreover, forany vector x 2 RjNj, we denote by x(S) the value

Pi2Sxi,

where S # N is a coalition.A feasible payoff profile (or pre-imputation) of G is a vec-

tor x 2 RjNj such that x(N) = C(N). An imputation of G is afeasible cost profile x 2 RjNj such that xi 6 C({i}), for eachi 2 N. This condition is usually called individual rationality.In our application, recall that every player i 2 N is associ-ated with the two constants cdi and DownloadBoundi,which model the cost for player i to download the full de-sired file from the network, and the maximum amount ofdata that i would like to download in the P2P process (ex-pressed as a fraction of the whole file). Thus, 0 6 Down-loadBoundi 6 1, where 1 means that i sets no a priorilimits on his possible download, and 0 means that i willnot download anything from the costly-link (therefore thisplayer will just participate in the sharing phase over theshort-range link). Therefore, by individual rationality, thetotal cost for every player i should be not larger thanC({i}) = p({i}) + DownloadBoundi � cd(i). The set of all impu-tations of the game G is denoted by X(G).

An outcome for G is an imputation from X(G) that spec-ifies the distribution of the cost to any player of the game.A typical requirement of a good outcome is to be ‘‘stable’’with respect to the possibility that subsets of players findconvenient to deviate from it, by forming alternative coali-tions and starting a P2P process on their own, in order toattain lower costs. The set of such stable outcomes isknown as the core of the game.

Definition 1 (Core [28]). The core CðGÞ of a cost TU gameG = hN,Ci is the set of all imputations1 x such that, for eachcoalition S # N, x(S) 6 C(S).

1 In the literature, feasible profiles are sometimes considered in place ofimputations. In fact, it is easily checked that the two forms are equivalent asfar as the definition of the core is concerned.

In words, the core is the set of all imputations that sat-isfy the cost upper-bound of all coalitions according to thecost function C. We say that if an imputation associatedwith a coalition is in the core then the coalition is stable;otherwise, we say it is unstable. Indeed, if y R CðGÞ, thereexists some coalition S such that y(S) > C(S). Therefore,players in the group S might leave the group N and buythe desired product on their own at the total cost C(S),which is less than what they were asked to pay accordingto the cost distribution y.

In general, the core of a game may be empty as well as itmay contain an infinite number of imputations. Animportant class of cost games where the core is alwaysnon-empty is the class of concave games (dually, theconvex games for value games). A game G is saidconcave if, for every pair of coalitions S and T,C(S [ T) + C(S \ T) 6 C(S) + C(T). It can be shown that thisholds if the cost function is submodular, that is, ifC(T [ {i}) � C(T) 6 C(S [ {i}) � C(S), for each pair of coali-tions S # T # Nn{i}.

However, even if the core is not empty, it remains theproblem of choosing an outcome out of possibly infinitemany candidates belonging to the core. Thus, solution con-cepts associated with unique profiles are usually desirablein applications. In particular, the Shapley value [29] is oneof the most used solution concepts in cost-sharing applica-tions (see, e.g., [24]).

Definition 2 (Shapley value [29]). The Shapley value of acost TU game G = hN,Ci is the pre-imputation of G assigningto every player i 2 N the following cost

/iðGÞ ¼1N!

XS # Nnfig

jSj!ðjNj � jSj � 1Þ!½CðS [ figÞ � CðSÞ�:

In words, the Shapley value assigns a cost to each playeri taking into account his ‘‘average marginal contribution’’,where the average is computed over all different se-quences according to which the grand coalition could bebuilt up from the empty coalition. This solution concepthas also a nice axiomatic characterization supporting itsnotion of fairness (it is the unique pre-imputation that sat-isfies the Symmetry, Dummy Player, and Additivity axi-oms). It is known that, in any concave game, the Shapleyvalue belongs to the core and thus it is a stable imputation.However, in the general case the Shapley value may beoutside the core, even if the core is not empty. Thus, in par-ticular, the Shapley value is not necessarily an imputation,and thus it may also violate the individual rationalitycondition.

Another approach to single out a fair outcome for TUgames is based on the notion of Nucleolus, first introducedby Schmeidler [30], and based on the lexicographical min-imization of the maximum unhappiness of coalitions.Although the Nucleolus in its current formulation has beendefined in 1969, it was later discovered that its ability todivide in a fair way scarce resources among competingagents was at the basis of some (previously) mysteriousrule in a Mishna of the Talmud attributed to Rabbi Nathan(about 1800 years ago), and in similar contested garmentrules [31]. Formally, given a cost game G = hN,Ci, a coalition


S # N and a cost allocation x, the excess (or unhappiness)of S w.r.t x is equal to eðS; xÞ ¼

Pi2Sxi � CðSÞ. For any impu-

tation x, define h(x) as the vector where the various ex-cesses of all coalitions (but the empty one) are arrangedin nonincreasing order:

hðxÞ ¼ ðeðS1; xÞ; eðS2; xÞ; . . . ; eðS2jNj�1; xÞÞ:

Let h(x)[i] denote the ith element of h(x).For a pair of imputations x and y, we say that h(x) is lex-

icographically smaller than h(y), denoted by h(x) � h(y), ifthere exists a positive integer q such that h(x)[i] = h(y)[i]for all i < q and h(x)[q] < h(y)[q].

Definition 3 (Nucleolus [30]). The Nucleolus NðGÞ of aTU game G is the set NðGÞ ¼ fx 2 XðGÞj 9= y 2 XðGÞs:t: hðyÞ � hðxÞg.

Therefore, this solution concept first cares about playersthat are less satisfied, then it cares about the less satisfiedamong the remaining coalitions, and so on for the rest ofthe coalitions, with the same approach. Interestingly, thereis a unique point that leads to the lexicographically mini-mum vector of excesses, that is, NðGÞ is in fact a singleton.Moreover, this unique outcome belongs to the Core, when-ever it is not empty, and usually offers a valid solution alsofor games with an empty core, so that the Nucleolus hasbeen considered as one of the most interesting solutionsto investigate [18].

A correct evaluation study on the effectiveness of GameTheory in designing ‘‘fair’’ cost allocation schemes in theenvisaged scenario derives from the selection of an appro-priate Game Theory solution concept to apply [27]. Differ-ent criteria have intrinsic differences in the fairness notionthey want to promote. Although many of them might beapplied to the wireless cooperation paradigm under study,the Nucleolus is preferred in this research, because minimiz-ing the maximum unhappiness of players fits well the appli-cation at hands. Moreover, we formally prove in this paperthat, for the class of games that best model our applicationscenario, the Nucleolus fulfills important game theoreticproperties. In particular, it is shown that for such a classof games the core is always non-empty. It follows thatfor these games the Nucleolus is not only a fair solution,but also a stable one (in that it belongs to the core of thegame), thus meeting two important requirements for theservice. The Shapley value [29] has been considered andstudied as well, but for the games associated with ourP2P application they sometimes exhibit the undesiredbehavior of not being a stable allocation.

3.2. Cooperative-download cost games

In this section, we describe a class of TU coalitionalgames that we call cooperative-download cost games (short:CDC games), defined by means of a suitable class of pricingfunctions determining the discount policy. Such gamesbest model our problem of assigning costs to nodes partic-ipating in the mediated P2P file-sharing process in a fair(and stable) way. In particular, we show that these gameshave always a non-empty core, even if they are not

concave. As a consequence, the Nucleolus of any CDC gameis always a stable imputation, while the Shapley value isnot necessarily an imputation (it depends on the chosenpricing function).

Formally, a CDC game G is a TU cost game hN,Ci, whereN is the group of players interested in buying some product(or bundle of products) according to the mediated P2Pdownload framework, and C is a cost function describedbelow.

First recall that the provider defines a suitable pricefunction p(S) to determine how to charge the nodes ofany coalition S for buying the jSj licenses for the productthey are cooperatively downloading, and recall that we as-sume this function to be sub-additive, that is, for every pairof coalitions S and T with S \ T = ;, p(S [ T) 6 p(S) + p(T). Infact, this property formalizes the usual business logic ‘‘themore licenses the more discount’’.

We are now ready to define the cost function of game G.With any coalition S # N, we associate a cost

CðSÞ ¼minfpðSÞþXi2S

ai � cdðiÞg

subject to :Xi2S

ai P 1

06ai6DownloadBoundi;8i2 S

Xi2S

ai � cdi PXi2S

cdi

!�GainConstraint

EnergyCoopiðaiÞ6EnergyNocoopi �EnergyConstrainti;8i2 S

TimeCoopiðaiÞ6 ti �TimeConstrainti;8i2 S

ð1Þ

In any optimal solution of the linear program above, theai control variable contains the (amount of) file fraction tobe downloaded by player i, in order to minimize the totalcost for the coalition S, while satisfying the problem con-straints in (1). In particular, note that we require that thewhole file can be reconstructed after the download of thesefractions (in fact, the constraint just checks the sizes of thefractions, as the actual subdivision of the file is performedlater by the Cooperation Server, respecting the informationin the ai values). Also, every player does not downloadmore data than it is allowed by the DownloadBoundi

parameter, thus meeting the individual rationality con-straint, and the GainConstraint of the network providershould be satisfied, as well. Finally, the data fractions tobe downloaded are required to meet also users’ require-ments in terms of energy consumption and time in cooper-ation which are limited by EnergyConstrainti andTimeConstrainti.

We require that the linear program (1) has a solution atleast for the case S = N. Indeed, in this case, the above opti-mization procedure provides the cost of the grand-coali-tion, and thus the total cost associated with any pre-imputation of the game. An unfeasible linear programwould mean that the constraints imposed by players andnetwork provider are too restrictive for the characteristicsof the involved players, and the cooperative downloadinvolving the whole group of players N cannot be executed.In such a situation the Cooperation server will enter in a


further procedure of coalition partition to find alternativecoalitions involving subsets of the nodes for which the con-straints are met and the cooperative download can be exe-cuted; details on this procedure are reported in Section 3.5.

For any other coalition S � N different from the grandcoalition, it is not necessarily required that a feasible solu-tion is found by the above linear program. In fact, in thesecases we can associate to the specific coalition the costCðSÞ ¼ pðSÞ þ

Pi2Scdi, that is, the cost when the nodes in

coalition S are not cooperating, i.e. the sum of the costsfor players in S assuming that each of them downloadsthe whole file on her/his own.

It could happen that some nodes have a ‘‘flat rate’’ forthe bandwidth cost. This situation can easily be modeledby setting to zero the constant function cdi in the model.Whenever this happens, and if player i does not limit itsmaximum possible download, the cost definition proce-dure would assign to such a node the whole download pro-cess, with the consequence of having a zero download costfor the whole cooperating group, with the additional ben-efit of a reduced content price. The subsequent fair costallocation will push the nodes with non-zero bandwidthcosts to strongly reward the node with the ‘‘flat rate’’. Thissituation could even lead to the possibility of actually‘‘earning money’’ in the process (in fact, note that suchnodes are probably paying higher fees for their flat-ratenetwork contracts). This is conceptually correct, and itshould be faced by considering, e.g., some bonus-basedmechanism. Noteworthy, in general, a similar situationcould also show up for scenarios with high differences inthe bandwidth costs among nodes and relatively low con-tent prices. However, for the sake of simplicity, we will notdeal with bonus/credits handling, as nothing changes inthe theoretical framework. In particular, in the experi-ments presented in this paper we avoid the use of verylow content prices with respect to download costs, andwe rather focus on the more interesting situation wherecontent and bandwidth cost levels are comparable.

3.2.1. Properties for the cooperative-download cost gamesRecall that a cost TU game is said sub-additive if its cost

function is sub-additive, that is, for every pair of coalitionsS and T with S \ T = ;, C(S [ T) 6 C(S) + C(T). For sub-additive games we usually say that the grand-coalitionforms. Indeed, in such games adding players to anycoalition is always cost-effective, which entails that thegrand-coalition is the most convenient configuration.Intuitively, we expect CDC games to have this property,since the business strategy of providers (‘‘the more licensesthe more discount’’) is modeled by the choice of sub-additive license (product) price functions. However, westill need a little proof of the property, because the pricefunction provides only a part of the total cost of coalitions(which is also determined by the optimization problemsolutions).

Proposition 1. Any cooperative-download cost game hN,Ciis sub-additive.

Proof. Let S and T be any pair of non-overlapping coali-tions. We know that, by definition, p(S [ T) 6 p(S) + p(T),because the price of product licenses is such that largercoalitions get larger discounts. It remains to consider thedownload cost, determined for each player i by theassigned file-fraction ai. Assume first that for S and Tdownload costs are defined according to the linear pro-gramming optimization (1), and consider any pair offeasible solutions �aS and �aT for the linear programs for Sand T, respectively. It is straightforward to check that theirunion is a feasible solution for the linear program forS [ T. Indeed, all the player constraints are clearlysatisfied by either solution, and the constraintP

i2S[Tai � cdi PP

i2S[T cdi� �

� GainConstraint is also satisfiedby linearity, as the two corresponding constraints for Sand T are satisfied by �aS and �aT . Therefore, in any optimalsolution �ao

S[T for the latter program, the download-compo-nent of the cost is at least as good as the sum of the down-load-cost components for �aS and �aT .

Finally, observe that the latter argument clearly holdsas well if the download costs for S or/and T are defined insuch a way that every player is assumed to download thewhole file (that is, if either linear program isunfeasible). h

We conclude the section by showing an importantproperty of the class of CDC games we are most interestedin, that is, the CDC games based on cardinality-discountcost-functions, called hereafter cardinality-discount CDCgames. These games are based on pricing functions that de-pend only on the cardinality jSj of the given coalition, andhave the following form:

pðSÞ ¼ price � jSj � 100� dðjSjÞ100

; ð2Þ

where price is the basic price of the product, that should bepaid by any single buyer not involved in any cooperativedownload, and d(�) is a non-decreasing function over thenaturals [0,N] which determines the (percentage) discountto be applied to the group S, given the number of users jSjbelonging to it. No special assumption is required for theform of d(�), but for its codomain [0,100] and the base casesd(0) = d(1) = 0 (no discount is given to the empty coalitionor to single noncooperating nodes).

Observe that the sub-additivity property holds for thisclass of functions, as required for legal pricing functionsfor CDC games. However it is worthwhile noting that thesefunctions are not concave in general, and hence the cardi-nality-discount CDC games based on them are not concave,too. Indeed, whether or not this property holds depends onthe choice of the specific discount function d(�). Neverthe-less, we are able to prove that, no matter on the choice ofthe discount function, these games (even if non-concave)have a non-empty core.

Proposition 2. Every cardinality-discount CDC game has anon-empty core, and thus its Nucleolus is always a stableimputation.


Proof. Let G = hN,Ci be a cardinality-discount CDC game,and let G0 be the modification of this game whose costfunction is C0(S) = C(S) � p(S), for every S # N. That is, thecost function of G0 is defined only by the linear optimiza-tion dealing with player constraints and the network pro-vider constraint, and it is independent of the productprice. Then, it is easy to see that G0 has a concave cost func-tion, because C(T [ {i}) � C(T) 6 C(S [ {i}) � C(S), for eachpair of coalitions S # T # Nn{i}. Indeed, such a newcomerplayer i adds the same constraints to both programs for Sand T, but the larger coalition T is clearly more flexible indealing with them. It follows that the core of G0 is notempty.

Let x0 be any imputation in the core of G0, and define apre-imputation x00 for G such that x00i ¼ x0i þ pðNÞ=jNj, forevery player i 2 N. That is, x00 is the same as x0 but now theprice of the product licenses are taken into account: it isuniformly distributed among all players. Let S # N be anyarbitrarily chosen coalition. We show that x00(S) 6 C(S)holds, hence x00 belongs to the core of G. By construction,x00ðSÞ ¼

Pi2Sx0i

� �þ jSj � pðNÞ=jNj 6 C0ðSÞ þ jSj � pðNÞ=jNj,

where the latter inequality follows from the fact that x0

belongs to the core of G0. Therefore,x00(S) 6 C(S) � p(S) + jSj � p(N)/jNj. To conclude, we justobserve that (�p(S) + jSj � p(N)/jNj) 6 0. Indeed, recall thatin cardinality discount CDC games the price function hasthe form pðSÞ ¼ price � jSj � 100�dðjSjÞ

100 for some non-decreasing discount function d(�). Therefore, we getpðNÞ=jNj ¼ price � 100�dðjNjÞ

100 6 pðSÞ=jSj ¼ price � 100�dðjSjÞ100 , because

the discount function d is non-decreasing with thecoalition cardinality, and thus the maximum possiblediscount is assigned to the grand-coalition N. h

Having a non-empty core and a stable Nucleolus is aremarkable property of cardinality-discount CDC games,as they seem quite appropriate to model the most frequentscenario for the proposed file sharing framework. On thecontrary, the Shapley value is not necessarily in the core,if the game is not concave.

3.3. Cost of product licenses for the nodes in the coalition

In this section, we conclude the description of the med-iated P2P process, by focusing on the last phase, where theCooperation Server actually assigns to every node i the partof the file to be downloaded. At this step, the Nucleolus xhas already been computed, and thus every player i knowshis total cost xi to get the product, comprising both the li-cense cost and the download cost.

Once the money issues are solved, we have the possibil-ity to perform a final optimization step possibly focusingon different aspects. For instance, while meeting the con-straints of the players and the total bandwidth cost to bepaid to the network provider (C(N) � p(N)), the actual fileshares to be downloaded may be assigned to nodes in sucha way that the download time over the cellular link is min-imized, in order to obtain the desired content in a shortertime. Other alternatives can be proposed as well, for in-stance one could minimize the total energy consumed overthe cellular link, or relax the constraints on the total band-width cost to be paid to the network provider when service

and network provider are not distinct entities, and so on.The time optimization may be obtained by minimizingthe maximum download-time over the participatingnodes. To this end, the Cooperation Server may performthe following linear-programming optimization:

min tmax

subject to :Xi2N

ai P 1

tmax P ai � ti; 8i 2 N

0 6 ai 6 DownloadBoundi; 8i 2 NXi2N

aicdi ¼ CðNÞ � pðNÞ

EnergyCoopiðaiÞ 6 EnergyNocoopi

� EnergyConstrainti; 8i 2 N

TimeCoopiðaiÞ 6 ti � TimeConstrainti; 8i 2 N

ð3Þ

where tmax is the variable to be minimized, whose feasible(lowest) values are determined by the greatest product ai -� ti, that is, by the slowest download. Then, from the valuesao

i ði 2 f1; . . . jNjgÞ of variables in any optimal solution of thelinear program (3), the Cooperation Server computes the ac-tual file parts, say bi, that any player i has to download overthe costly link. The transaction ends when every player ihas payed its license fee xi � ao

i � cdi, and all parts have beendownloaded. Note that the unique constraintP

i2Naicdi ¼ CðNÞ � pðNÞ suffices to deal with economic is-sues. For instance, it entails that the network provider’sGainConstraint is fulfilled, because it is so in the solutionleading to the computation of C(N), which determines thenetwork profit C(N) � p(N). Further constraints to be con-sidered for this final optimization are the constraints onthe energy consumption and the time in the cooperativecontent download as defined by the players.

3.4. Energy consumption and time constraints definition

While the main focus for the proposed model is on themonetary costs related to the cooperative content down-load, the proposed framework foresees the possibility forthe users to define energy consumption and time con-straints when joining a cooperative content download.The Cooperation Server will thus compute the energy con-sumption and the time needed to receive the content incooperation for the nodes. These will then be comparedto the non-cooperative case to check whether the wishedconstraints are met for the nodes. The framework can workwith any short-range link, but in order to have some real-istic models and figures in the performance evaluation weneed to focus the attention on a specific network, forexample Bluetooth. While the interested reader can finddetails for the energy consumption model for the cellu-lar-Bluetooth cooperative setting in [23], we will briefly re-port here the main findings needed in this paper.

In a Bluetooth piconet, the number of nodes simulta-neously active is limited to 8, where one node acts as mas-ter and the remaining nodes act as slaves. No direct slave-to-slave communications are possible and all transmis-


sions go through the master. A round robin scheduling ofthe involved nodes is performed [32] and the master canperform broadcast communications to the slaves. The nodeplaying the master role is a key factor in defining the en-ergy consumption and the required time in cooperation.Consequently, when the Cooperation Server will performthe proposed linear optimization, it will also consider thedifferent potential master–slave configurations.

Let us define the energy when noncooperating, Ener-gyNocoopi, as the energy consumption for node i whendownloading the whole content over its costly cellular link,and EnergyCoopi as the energy consumption for node i incooperation. The definition of EnergyNocoopi is straightfor-ward: EnergyNocoopi ¼ Pci

Rci� X; where Pci and Rci are respec-

tively the power consumption and the data rate on thecellular link for node i, and X is total content size (ex-pressed in Kbyte). For what concerns the EnergyCoopi term,both cellular energy consumption and Bluetooth energyconsumption have to be considered. In the reference archi-tecture, nodes first download all data over the cellular linkbefore sharing them over the short-range link. The energyconsumption on the cellular link is simply computed as themean cellular power consumption multiplied by the as-signed file fraction and divided by the mean link through-put. Instead, a detailed analysis of the Bluetooth link isneeded since, over the time, the number and type of packettransmissionsnreceptions of a node depend on several fac-tors. Summarizing the results found in [23], the expressionof the energy consumption in cooperation can be written asa function of the file fraction for each node i to be down-loaded over the cellular link, ai, and on the role r playedin the piconet (master or slave), as reported in Eq. (4). InEq. (4), the first term is the energy consumption on the cel-lular link, the next three terms represent the energy con-sumption respectively in transmitting data, in receivingdata, and during the idle time on the Bluetooth link anda final term measures the energy consumption for theGPS positioning of each node.

EnergyCoopiðaiÞ ¼ EdiðaiÞ þ Ebtiðr;aiÞ þ Ebriðr;aiÞþ Ebiiðr;aiÞ þ Ep ð4Þ

The Edi(ai) term is the energy consumption in down-loading the assigned file-share ai over the cellular link (thisterm is not depending on the master or slave role in theBluetooth piconet). This is defined as EdiðaiÞ ¼ Pci

Rci� X � ai,

where X is the data size, Pci and Rci are the power con-sumption and the throughput on the cellular link for nodei, respectively. The Ep term in Eq. (4), is the energy con-sumed by the nodes to gather their GPS positioning. Forthe further terms of Eq. (4) the values for the Bluetoothspecific parameters are set according to the standard [32]and the exact definition is taken from the model presentedin [23].

When looking instead at the time needed to receive thecontent, as introduced earlier in this section, ti is the timeneeded for node i to download the whole content over itscellular link. Then, let us define TimeCoopi as the timeneeded for node i to receive the content in cooperation.

When cooperating the devices will first download the as-signed file fractions over their cellular links and then sharethem over the Bluetooth link. During the first phase of cel-lular downloading, they can, in parallel, setup the Blue-tooth piconet. Therefore, the time in cooperation is equalfor all nodes i and can be computed as the sum of maxi-mum time spent on the cellular link by the nodes, the timeneeded to distribute the data over the Bluetooth link, and asmall contribution of time for the Cooperation Server tocompute the solution:

TimeCoop ¼ tmax þ TimeBT þ TimeServer ð5Þ

tmax is defined by the linear program in Eq. (3); the timeon the Bluetooth link TimeBT is given by the number ofRound Robin scheduling cycles needed to distribute the to-tal data for a given packet payload (further details on thiscomputation can be found in [8]); the time for the Cooper-ation Server to compute the solution TimeServer is here as-sumed equal to 19s as this is the worst case value for acomputer with mean hardware capabilities when it is nec-essary to compute the optimization problem for all possi-ble coalitions to find solutions meeting all the constraintsfor the problem.

3.5. Coalition partition definition

As discussed earlier in this section, the different con-straints set by the users and/or by the network may causethe linear optimization not to find a valid solution for thegrand coalition. Moreover, if the Shapley value is the cho-sen cost-allocation solution, then the property of beingoutside the (non-empty) core may be considered unaccept-able. To deal with these cases, the Cooperation Server maybe equipped with a strategy to find alternative groups ofplayers to cooperate successfully. The proposed policy isto exclude iteratively some of the nodes until a first coali-tion is found where all the requirements are met. If morealternatives are meeting the constraints, then a furtherpolicy should be introduced to select the preferred coali-tion. In this framework, we adopt the well-known conceptof maximizing the social welfare [15], whereby the coali-tions that maximize the total monetary savings (for them-selves) are preferred. In more detail, if for the coalitioninvolving N nodes a valid solution cannot be found, thensmaller coalitions are considered. Whenever a coalitionwith the required properties is formed (clearly, it will bea maximal one), the process restarts with the excludedusers, until a partition p of the players N in coalitions, alsocalled a coalition structure [15], is found. Note that stan-dard game theoretic solution concepts for coalitional struc-tures, such as the core, consider stability conditions also onsets of players belonging to different elements of the parti-tion p [33]. However, such inter-structure conditions leadto high computational costs that are not suitable for thepractical applications we have in mind. Therefore, weadopt here a simplified approach where each element pi

of the structure induces a distinct (sub) game which is ana-lyzed separately from the others (being defined over dis-joint sets of players).


3.6. Remarks on practical implementation and computationalanalysis

In this section we briefly discuss practical issues in apossible implementation of the proposed service. TheCooperation Server promotes the service and collects sub-scription of users interested in its product(s). The nodesregistering to the service will agree to the term and condi-tions for the service. Product licenses will be active onlyafter the cooperating process is ended. Thus, in case of amisbehavior of a node in cooperation, this can be easily de-tected, and (for instance) the license of such a node may beset to an invalid state by the provider. Note that a basicimplementation of cooperative-downloading may be de-signed as an atomic transaction, as the involved group ofusers is intended to be static during the process. In this ap-proach, if some node goes down during the process and isnot able to recover within some reasonable time-out, thenthe process fails and a restart or some form of renegotia-tion is required (indeed other nodes may then be accepted,and if no further node comes in, then the price of the li-censes may be higher for the resulting smaller group).

For each service subscriber, a user profile will be de-fined collecting basic information provided when the de-vice registers to the service. In general the CooperationServer could be available on the Internet and accessibleby the service subscribers from any location. The Coopera-tion Server will then wait for nodes to contact him provid-ing all information needed for the service, including thegeographic position of the node (e.g., determined throughits GPS coordinates or any other positioning technique). Arequirement for the nodes to be considered as part of acommon content download, is that to be interested in thesame content (possibly, a bundle of products) and in mu-tual coverage for a cooperative short-range link. Samplescenarios where these conditions are fulfilled can begroups of friends in aggregation places (such as a Univer-sity campus) to exchange and download books, music orother contents.

Once the users have provided the required information,the Cooperation Server notifies each device about: involveddevices and how they are clustered, the masternslave roleplayed by each node in the piconet (only in the analyzedcase of using Bluetooth as short-range link), the exact datashare to download through cellular links and the corre-sponding cost, and the content price that will be chargedto the user account. All cooperating devices will then firstdownload the assigned file fractions over their cellularlinks and then share them over the short-range link. Duringthe first phase of cellular downloading, they can, in paral-lel, setup the Bluetooth piconet. Bluetooth limits the num-ber of nodes simultaneously active on a piconet to 8;therefore, the Cooperation Server collects a maximum num-ber of eight candidates requiring the service within a lim-ited period of time, before computing the solutions. If aninth device contacts it, then a new process is started.Obviously if less than eight nodes are interested, thesecould as well cooperate (for instance, a suitable timer candetermine a time interval wherein the Cooperation Servercollects the cooperation requests before starting the coop-eration process). Finally, it is worth spending some words

concerning the computational cost of the presented frame-work. The Nucleolus computation is actually playing aminor role in the overall computational costs, once the costfunction is known. In fact, the major contribution to thecomputational cost is given by the linear programmingoptimization step that is performed for every possible coa-lition, which means 2jNj � 1 times. Moreover, for each coa-lition, a number of minimization problems proportional tothe number of nodes k in the coalition is required to definethe master and slave roles. The total number of minimiza-

tion problems is: nminðNÞ ¼PN

k¼2k Nk

� �. However, it is

worth mentioning that executing the introduced frame-work requires a few seconds, as tested with a basic hard-ware deployment; this order of magnitude is definitelyacceptable for the proposed file sharing service.

4. Experimental evaluation

A numerical evaluation of the model is conducted to ob-serve the behavior of the envisaged paradigm under a widerange of system configurations. Main objective is to vali-date the ‘‘mediated wireless cooperation’’ by looking bothat cost savings for the single nodes (compared to a stand-alone classical content download) and at providers’ profits,under different conditions. It will also clearly emerge that agame theoretic approach based on the Nucleolus is pre-ferred to standard optimization criteria, as far as the fair-ness perceived by users is concerned. The resultspresented next are related to Bluetooth as short-range link,but the overall framework can equally work with any othershort-range technology.

We considered sample cases where cooperating nodeshave different cellular throughput levels. All presentedcases assume that nodes have a time-based billing agree-ment with the provider; we express this cost in terms ofa given amount of generic Cost Units per second (CU). Notethat from these measurements and from the size of theproduct file we may immediately compute the values cdi

and ti characterizing the device features of any node i. Alsothe alternative billing policy foreseeing that nodes arecharged on a data-amount basis has been investigated. Asthere is no conceptual difference, the results will refer tothe first case only. In particular, the cost per second is setto 0.05 cost units, the file size is 100 Mbyte, and the basiccontent price price is equal to 400 cost units. Concerningthe power consumption on both the cellular link and theBluetooth interface, the values used in the present paperresult from measurement campaigns (conducted on N95Nokia smartphones). In particular, different values ofpower consumption have been measured for a device con-nected to a 2.5G or to a beyond 2.5G system (400 mW for2.5G, 1400 mW for beyond 2.5G and we assume 250 kbpsthe maximum data rate value for a 2.5G connection). Forthe Bluetooth the adopted values are 178.2 mW, 108 mWand 59.4 mW in transmission, reception and idle timerespectively. Finally, the energy consumed by the nodesto gather their GPS positioning is set according to resultsin [34], whereby the energy consumption for a NokiaN95 smartphone is equal to 13.32 J in the best case.

Fig. 2. Content discount function for multi-license products.


It is assumed that the Cooperation Server chooses a pricefunction of the type described in Section 3.2.1. More specif-ically, we next consider cardinality-discount CDC gameswhose discount functions are based on the functions pro-posed in [35], suitably adapted to the scope. Fig. 2 reportsthe discount proposed by the content provider w.r.t. to thenormal basic price for different number of nodes. The plot-ted equation is given by

dqðjSjÞ ¼ Maxdiscount �exp½�ðjSj � 1Þ=q� � 1

exp½�ðjSjmax � 1Þ=q� � 1with q – Infinity

ð6Þ

where jSj and jSjmax are respectively the cardinality of thecoalition and the maximum cardinality (when not differ-ently stated, in our experiments this is set to 8), q deter-mines the discount amount for either larger or smallercoalitions, Maxdiscount represents the highest discount pro-posed by the provider which is set here to 50. It is easyto see from the formula that the highest 50% discount is of-fered when the coalition size jSj is equal to jSjmax, while nodiscount is given to the noncooperating nodes when jSj isequal to 1.

Based on the above discounts, we get the followingclass of cardinality-discount price-functions:

pqðSÞ ¼ price � jSj � 100� dqðjSjÞ100

ð7Þ

We use these price functions for the experiments thatillustrate the proposed framework. In particular, we focuson the case with q = 2, as this offers higher savings imme-diately, encouraging the users to join cooperating groupsalso of very small sizes. Interestingly, for positive q valuesand in particular for the chosen q = 2 value, sub-modular-ity does not hold for such a function, because the marginaldiscount obtained by larger coalitions is smaller than themarginal discount obtained by smaller coalitions (see

Fig. 2). Thus, the considered games are not concave, butfrom Proposition 2 we know that the core is always notempty.

The Cooperation Server is made aware of the limit on theamount of data to be downloaded in the P2P applicationimposed by the nodes. In general each node could requestdifferent values for this parameter, but for simplicity in thepresentation of the results and to better discuss the influ-ence of this parameter, we assume all nodes having thesame DownloadBoundi, hereafter just calledDownloadBound.

Several throughput distributions for the nodes can beconsidered. A straightforward test scenario is character-ized by ‘‘homogeneous’’ nodes, i.e. nodes with the samecellular throughput level. In this case, if there are no fur-ther constraints, the solution found by the bandwidth-costoptimization procedure performed by the service coordi-nator assigns an equal share, hence an equal cost, to allnodes. Such a homogeneous cost allocation is in fact theNucleolus of the associated game and it belongs to the core(in fact, it is also the Shapley value), and no further analysisand cost compensations are required.

For any scenario different from the cited ‘‘homoge-neous’’ one, the proposed game theoretic model provesthat defining a fair cost allocation for the participatingnodes is unavoidable. During the study, a wide range ofscenarios with variable throughput distributions for thenodes have been considered. The results are also con-trasted with the possible reasonable outputs of some alter-native approach, which rely on an optimization only (i.e.,not based on game theoretic concepts). The sample scenar-ios presented in the remaining part of the paper are se-lected to give the reader a broad overview of theproposed framework behavior. They are characterized byhalf of the nodes with a cellular throughput ofT = 100 kbps, while the throughput of the remaining nodesequal to (T + d) kbps, with d variable. Clearly, a similar anal-ysis can be repeated for different nodes configurations,obtaining similar plots.


4.1. File-shares assignment, node costs, and service providerprofit

With reference to the output of the cooperative game,let us focus on the cost assignment to nodes, which is alsoequal to providers’ profit. The cost assigned to each node isa combination of the content license cost and the costderiving from the download of the assigned file-share overthe cellular links. Of course, these values directly dependon DownloadBound and node throughput values, while alsothe GainConstraint of the network provider influences thefinal results. These dependencies are investigated next,while it is assumed the nodes have not set stringent con-straints on the energy consumption and time delay incooperation.

In Fig. 3 it is shown how the file-shares to be down-loaded by nodes, hence their download costs, change withthe parameter DownloadBound and the GainConstraint; thisbehavior is highlighted in sample cases in whichd = 100 kbps. Recall that such file-shares are assigned bythe final minimization step, as described in Section 3.3.

Let us focus first on the case with GainConstraint (inshort GC) set to zero and analyze the influence of theDownloadBound (in short DB), left side of the plot. To min-imize the maximum download time according to linearprogram (3), the solution is to assign larger portions of datato be downloaded to the four nodes with higher cellularthroughput (nodes 5–8 in the scenario). For any scenariowith DownloadBound P 0.25 these four nodes will down-load 1/4 of the file each. When the nodes set more strin-gent constraints on the DownloadBound, also the othernodes are involved. For any value DownloadBound <0.125(that is maximum 1/8 of the file) no feasible solution canbe found, since the total number of nodes is 8. Note thatsimilar considerations hold for different values of the totalnumber of nodes in the coalition; obviously, these lead todifferent limiting values for the DownloadBound value.Moreover, it is worth commenting that in a more generalsystem setting, where all values of nodes’ cellular through-put are different, again to minimize the maximum down-load time according to linear program (3), the solution isto assign a larger portion of file to download to the nodes

Fig. 3. Influence of DownloadBound (DB) and GainConstraint (GC) on the

with higher cellular throughput as far as the Download-Bound constraint allows it.

To assess the impact of the GainConstraint set by thenetwork, we analyze the case where DownloadBound isset to 0.25. We can compare the scenario with GainCon-straint not set (the third case in the left side of the plot inFig. 3) and the scenario corresponding to the results re-ported on the right side of the plot in Fig. 3. Two main ef-fects of an increase in the GainConstraint parameteremerge. First, the nodes with a less performing cellular linkare now also involved in the content download over thecellular link. This is justified by the increase in the band-width income required by the network provider. Whenthe GainConstraint increases even more, the second effectis that the cooperating cluster is forced to download morethan one copy of the total file (e.g. two copies are down-loaded when GC = 0.25).

Next, we want to investigate on the costs repartitionamong the nodes in the considered scenarios. In Fig. 4the cost for the content license and the content downloadis reported for the nodes in the sample scenarios withd = 100 kbps, GainConstraint = 0 and the DownloadBoundset to one of the following values: 0, 0.125, 0.2, 0.25. InFig. 5 instead, the same information is reported when Gain-Constraint assumes one of the following values 0, 0.125,0.2, 0.25, while d = 100 kbps and DownloadBound = 0. Whatcan be observed in both of the figures is that a node havinghigher costs for the content download, will pay a smallercontribution for the content license. This observation hasa general validity also in a system setting with more differ-entiated values of cellular throughput for the nodes. It canalso be observed that the cost for the content is often high-er, for some nodes, than the cost given by the price func-tion pq(S). The reason for this is that it has also to coverthe costs for the node ’’more devoted to the contentdownload’’.

A numerical example is given to clarify the latter com-ment. Let us focus on a node i with cellular throughput100 kbps and a node j with cellular throughput 200 kbps.For the specific bandwidth cost and file size settings(0.05 CU per second and 100 MB respectively), if nodesdo not cooperate then they will be charged the following

file portions assigned for download to nodes; d is set to 100 kbps.

Fig. 4. Cost distribution among the nodes according to the Nucleolus solution for different values of DownloadBound and d = 100 kbps, GainConstraint = 0.

Fig. 5. Cost distribution for the nodes according to the Nucleolus solution for different values of GainConstraint and d = 100 kbps, DownloadBound = 0.25.


basic costs: p(i) + cd(i) = 400 + 400 CU = 800 CU;p(j) + cd(j) = 400 + 200 CU = 600 CU. The nodes may decideto contribute to the cooperative download by fixing theupper bound on their possible downloads to 0.2, and ex-pect to have the following maximum costs: pq(i) +DownloadBound � cd(i) = 200 + 80 = 280 CU; pq(j) + Down-loadBound � cd(j) = 200 + 40 = 240 CU. This means an over-all saving for the service equal to: Saving(i) = 520 CU(corresponding to a 65% saving) and Saving(j) = 360 CU(corresponding to a 60% saving). If we now observe the costassigned to these nodes by Nucleolus (see Fig. 4), we noticea cost of 250 CU and of 200 CU for nodes i and j, respec-tively. These results lead to the following final savingsw.r.t. to the non-cooperating case: Savingfair(i) = 550 CU(corresponding to a 69% saving) and Savingfair(j) = 400 CU(corresponding to a 67% saving). This simple computationdemonstrates that the final savings meet the user

constraints, and this is done in a fair way, i.e. by consider-ing the ‘‘merits’’ of each node.

The next analysis presented in Fig. 6 shows the influ-ence of the DownloadBound and the GainConstraint param-eters on the total cost C(N), which equals the totalproviders’ profit. This value decreases with increasing val-ues of the DownloadBound, since for lower DownloadBoundvalues also nodes with lower bandwidth costs have to beinvolved in the download phase. On the other hand, it in-creases with the GainConstraint parameter. Interesting toobserve is how two of the plots overlap completely (thecase with DB = 0.25; GC = 0.125 and the case withDB = 0.125; GC = 0) even if the settings are different andthe specific cost allocations to the nodes are different asshown in previous plots. Moreover, in Fig. 6, the influenceof d value is also plotted. The decreasing trend when d isincreasing is expected, because higher throughput values

Fig. 6. Content and network provider profit in cooperation, variable d according to the Nucleolus solution.


mean faster content downloads and, thus, lower profits forthe provider (as costs are assumed to be time-based).

4.2. Nucleolus vs. proportional cost distributions

Previous plots testify to the good behavior of theNucleolus in terms of cost savings, we next focus in moredetail on fairness aspects, when this approach is comparedwith alternative solutions.

In particular, one may wonder whether alternative rea-sonable approaches exist that are not based on game the-oretic principles. We already observed that traditionaloptimization techniques aim at minimizing (or maximiz-ing) some measure like the total cost, but typically donot care about fairness in the final cost assignment to theparticipating nodes. According to the specific applicationand objective, different optimal solutions can be proposed(e.g. for solutions oriented to delay in content distribution[8]).

In our case, to compare such techniques with theNucleolus solution, we next consider the following simplecost-distribution, that we call Optimization + ProportionalCosts. Following a first step, where the optimal cost C(N)is computed according to the linear program presented inEq. (1), this cost is then assigned to nodes, proportionallyto the bandwidth costs, i.e. according to the cdi parameterfor each node: xpr

i ¼ CðNÞ � cdiPj2N

cdj, for each i 2 N.

In Table 1 a comparison is presented among this pro-portional cost solution, the solution given by the linearprogram optimization, and the Nucleolus. Two samplecases are presented, but similar results are obtained formany other cases. In particular, the presented cases referto scenarios where DownloadBound is set to 0.25 for allnodes, GainConstraint is set to zero, nodes 1–4 have cellularrate Rc1 = 100 kbps and nodes 5–8 have cellular rate Rc2 =(100 + d) kbps with d either equal to 100 or 1500. Besidesthe differences in the cost allocation, the experiment aimsat observing whether the proposed allocation is stableaccording to the core and if it actually meets the cost/sav-ings constraints set by the users. As it can be observed, the

optimal solution is not always a stable allocation, while theproportional cost allocation is not always meeting the con-straints for the nodes.

4.3. Considerations on the Shapley value as alternative costallocation method

Note that our framework is rather independent fromthe particular game theoretic solution concept, as long asits notion of fairness fits well the proposed application.We thus briefly discuss the possible results obtainablewith cost allocations following the Shapley value, a well-known solution concept which is a valid alternative, andwhose main properties have been described in Section 3.1.

The numerical evaluation presented in the previous sec-tions has been repeated by considering the Shapley valueinstead of the Nucleolus. In some experiments, the Shapleyvalue is not a stable imputation for the coalition involvingall the nodes, as it is outside the core and does not fulfillthe individual rationality. This is not surprising, if we con-sider that our cost games are not concave for the chosenprice function. However, as proved in Proposition 2, thecore is not empty and hence the Nucleolus does not sufferfrom those drawbacks. Another observation is that, whenusing the Shapley value, the proposed framework requiresa higher computational time. This varies with the differentpresented cases, but even increases up to 70% in the timedelay with respect to the Nucleolus case have beenreached. These considerations support our choice of focus-ing on the Nucleolus as the preferred solution concept forthe proposed framework.

When the Shapley value is not in the core for the gameinvolving all the nodes, alternative coalitions are consid-ered with a reduced number of cooperating nodes. Themain consequence is that the savings introduced for thenodes are reduced. This is clearly plotted in Fig. 7, wherethe average cost savings per node when using the Shapleyvalue or the Nucleolus are considered, in different scenar-ios with variable d and GainConstraint parameters, andDownloadBound = 0.25. In all the plotted cases, the Shapley

Table 1Comparison among optimal, proportional, and game theoretic cost allocations; DownloadBound is set to 0.25 for all nodes, GainConstraint is set to zero, nodes1–4 have cellular rate Rc1 = 100 kbps and nodes 5–8 have cellular rate Rc2 = (100 + d) kbps.

d = 100 kbps d = 1500 kbps

Nodes 1–4 Nodes 5–8 Nodes 1–4 Nodes 5–8

Cost per node (CU) 200 250 200 206.25Savings per node (CU) 600 350 600 218.75

Optimization Constraints met Yes Yes Yes YesStable Yes Yes No No

Cost per node (CU) 300 150 382.3 23.9Savings per node (CU) 500 450 417.6 401.1

Proportional Constraints met Yes Yes No YesStable Yes Yes Yes Yes

Cost per node (CU) 250 200 250 156.25Savings per node (CU) 550 400 550 268.75

Nucleolus Constraints met Yes Yes Yes YesStable Yes Yes Yes Yes

Fig. 7. Shapley value vs. Nucleolus: average per node savings with variable d, DownloadBound = 0.25.


value does not guarantee that the grand coalition involvingall 8 nodes is formed. In these cases, either 1, 2, 3 or 4nodes are excluded from the coalition and, thus, lower sav-ings are obtained when compared to the Nucleolus solu-tions. Only in a few cases a second coalition is formedthat involves the excluded nodes. In particular, this hap-pens for all cases with d P 1100 and GC = 0.2 andGC = 0.25, where always two coalitions of four nodes areformed. For the other scenarios, the GC = 0.2 andGC = 0.25 cases register a lower average cost saving w.r.t.the case with GC = 0.125. The reason for this is related tothe coalition being formed and the nodes being excludedfrom cooperation. As an example, let us consider thed = 200 scenario. With GC = 0.125 a 6-nodes coalition isformed where two nodes with a higher cellular throughputand thus lower costs in non-cooperation are excluded;with GC = 0.2 a 5-nodes coalition is formed where nowthree nodes with low costs in non-cooperation are ex-cluded; with GC = 0.25 a 6-nodes coalition is formed wherethis time two nodes are excluded with high costs in non-

cooperation. Similar considerations can be made for anyother case.

4.4. Savings for different coalition sizes and discount functionsettings

Results presented in previous sections have focused onthe behavior of the grand coalition where fair cost alloca-tions are found. Next, we first give the reader some insightson the benefits the nodes gain in joining larger coalitionsinstead of smaller sub-coalition. Then, we will show howthe maximum coalition size set by the service provider inthe discount function influences the benefits for cooperat-ing users and provider.

Fig. 8 shows the average per node savings obtained injoining coalitions of different sizes. The grand coalition sizeis jSj = 8, while also the sub-coalitions are considered with2, 4, or 6 nodes (also these coalitions have the same cellu-lar throughput combinations as for the grand coalition).The DownloadBound and the GainConstraint are not set for

Fig. 8. Average per node savings for different coalition sizes jSj with variable d.


the plotted case for simplicity. As it clearly appears fromthe plots, and as expected, nodes have always higher mon-etary savings in joining larger coalitions.

The subsequent analysis focuses on the influence thatthe maximum acceptable coalition size, set by the serviceprovider in the definition of the discount function, has onthe final monetary savings for the nodes and the overallprofits for the service provider. This analysis has also thefurther objective to investigate on the possible trade-offbetween the service provider and the cooperating nodesinterests. These are clearly conflicting like their objectives,with the service provider wishing to maximize the mone-tary incomes for the service, and the users wishing to min-imize the service costs. Going into details, the serviceprovider can decide to limit the maximum coalition sizeby tuning the value for jSjmax in Eq. (6). Changing this set-ting, the first effect is a modification in the discount func-

Fig. 9. Average per node network profit and average saving per node, for diffe

tion plotted in Fig. 2, with a maximum discount obtainedat the corresponding jSjmax value. The jSjmax values we con-sidered for this analysis are 2, 4, 6 or 8, while the choice interms of q for the discount function is kept constant,namely q = 2.

We consider some sample scenarios with either Down-loadBound = 0 (see Fig. 9) or DownloadBound = 0.25 (seeFig. 10), where half of the nodes have a cellular throughputlevel Rc1 = 100 kbps and the second half have a cellular rateRc2 = (100 + d) kbps with d either equal to 100 or 1500. Asexpected, the results in Fig. 9 show that the service pro-vider profits increase with lower values of jSjmax, whilethe users savings increase with larger values of jSjmax.Moreover, a generally valid trade-off between the networkprovider and the users interest cannot be found. For in-stance, Fig. 9 shows that, when considering coalitions ofonly two nodes (i.e. with jSjmax = 2), the absolute values

rent coalition sizes and jSjmax in Eq. (6) with q = 2; DownloadBound = 0.

Fig. 10. Average per node network profit and average saving per node, for different coalition sizes and jSjmax in Eq. (6) with q = 2; DownloadBound = 0.25.

Table 2Impact of the energy savings constraint on the cooperative contentdownload; DownloadBound, GainConstraint and Time constraints are notset, nodes 1–4 have cellular rate Rc1 = 100 kbps and nodes 5–8 have cellularrate Rc2 = 200 kbps.

Energy constraint

0.2 0.4 0.6 0.8 1

Cooperative coalition size – 8 8 8 8Avg energy savings (J/Kbit) – 2.22 2.27 2.27 2.27Avg monetary savings (CU) – 468 475 475 475Max time delay (%) – 44 31 31 31


of the objective functions for the service provider and theusers are the closest. By increasing the value of jSjmax,and thus the maximum coalition size, the two objectivefunctions diverge. The observed trends for a variable valueof jSjmax, suggest to use the case with jSjmax = 4 as a poten-tial trade-off point. Nevertheless, when changing theDownloadBound value, like in Fig. 10, the situation com-pletely changes and the same conclusions are not validanymore. Thus, we can conclude that the discount functionproposed by the service provider has definitely a keyimportance in the definition of the system performance.Unfortunately, it is not possible to design a generally validfunction that guarantees a trade-off between service pro-vider and user objectives in all potential scenarios.

Table 3Impact of the download time constraint on the cooperative content download; Dowhave cellular rate Rc1 = 100 kbps and nodes 5–8 have cellular rate Rc2 = 200 kbps.

Time constraint

0.4 0.6 0.8

Cooperative coalition size – 4 4j2j2Avg energy savings (J/Kbit) – 2.6 2.6j199j19Avg monetary savings (CU) - 460 460j181j1Max time delay (%) – �42.5 �42.5j�26

4.5. Influence of the energy consumption and time constraints

In the analysis presented so far, the focus has mainlybeen on monetary savings introduced by the proposedframework and the influence of the related constraints. Inthis section, the attention is put on the further constraintsthe nodes can set when joining the cooperative service,namely the energy consumption and the time constraints.To best highlight the impact of these two constraints, wepresent sample scenarios where the DownloadBound andthe GainConstraint are not influencing the solutions. Weconsider only the Nucleolus solution for a sample scenariowhere nodes 1–4 have cellular rate Rc1 = 100 kbps andnodes 5–8 have cellular rate Rc2 = 200 kbps (a similar anal-ysis can be repeated for other cases) and the energy con-sumption and time constraints are equal for all nodes, forsimplicity.

In Table 2 the values of the main performance indexesare reported for increasing values of the energy consump-tion constraint set by the users, while no time constraint isconsidered. In particular, energy consumption constraintvalues are considered in the range 0.2–1 (see the problemdefinition in Eq. (1)). As it clearly emerges from the results,the cooperative content download actually introduces en-ergy savings for the nodes. This is not a surprising result,see e.g. [23]. What can be observed is that for energy con-straints from 0.6 and above no difference in the final per-formances is obtained. Moreover, for an energy constraint

nloadBound, GainConstraint and Energy constraints are not set, nodes 1–4

1 1.2 1.4 1.6

5j3 7 8 89 1.4j2.03 2.3 2.3 2.3

81 378j397 474 475 475.6 j�26.6 15j�31 20 31 31


of 0.2 the nodes will actually not cooperate, while in allother cases always the grand coalition of 8 nodes is formedand both energy and monetary savings are obtained. Final-ly, also the maximum time delay experienced by the nodesin cooperation is reported. What emerges is that a maxi-mum delay of 44% is reached, which is experienced bythe nodes with the fastest cellular throughput (the nodeswith Rc2 = 200 kbps in the specific case).

In Table 3 the same performance indexes are presentedfor variable values of the time constraint set by the users,while no energy constraints is set. Also for the time con-straint, cases exist where actually a gain is obtained incooperation (see the cases with negative delay values re-ported in the Table). For time constraint values equal to0.4 and below no cooperative download can be activateddue to the stringent constraints. In the other cases, instead,the main effect of setting the constraint is that smallercoalitions are formed and different average energy savingand monetary saving are obtained by the nodes in thecoalitions. Finally, when the time constraint is not so strin-gent (from 1.4 and beyond) again the grand coalition of 8nodes is formed and no influence of the time constrainton the results is observed.

5. Conclusions

This paper uses the powerful mathematical frameworkof Game Theory to enable a mediated business model,according to which a provider promotes itself as a servicecoordinator for a cooperative file sharing service. Nodescooperatively download a file of common interest overtheir cellular links and share it over a cost-free short-rangelink. The idea is to give the provider the opportunity to sella larger number of licenses by proposing suitable group-discounts for content to be downloaded. On the otherhand, nodes have significant cost savings when comparedto a stand-alone download of the whole content, as theybenefit both of a reduced cost for the content and of anoptimal bandwidth cost-distribution over the cellular link.Moreover, they benefit from a ‘‘legal’’ service with theadditional important guarantee that costs are fairly as-signed to nodes and there are no free riders. Since fairnessand stability of a solution is of utmost importance, theuse of Game Theory to model the cost distribution problemproved to be an effective approach. Based on a coalitionaltransferable-utility cost game, the Nucleolus has beenadopted as a valid solution to determine the fair cost allo-cations for the cooperative cluster. A number of propertiesof the proposed approach are shown and commented un-der a wide range of sample operational conditions.

Acknowledgments

Special thanks go to Miguel Ángel Mirás Calvo and Este-la Sánchez Rodríguez from University of Vigo and to JeanDerks from University of Maastricht for their importantsuggestions and the Matlab toolboxes they have kindlyshared with us for the numerical evaluation campaign forthis paper.

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Leonardo Militano is a research fellow at theUniversity ‘‘Mediterranea’’ of Reggio Calabria,Italy. He received a Ms. degree in Telecom-munications Engineering from the Universityof Reggio Calabria, in 2006 and his Ph.D inTelecommunications Engineering in 2010 atthe same university. He has been a visitingPh.D student at the Mobile Device group atUniversity of Aalborg, Denmark. His majorareas of research are wireless networks anduser cooperation.

Antonio Iera is a Full Professor of Telecom-munications at the University ‘‘Mediterranea’’of Reggio Calabria, Italy. He graduated inComputer Engineering in 1991 and received aPh.D. degree from the University of Calabria.From 1994 to 1995 he has been with SiemensAG in Munich, Germany to participate to theRACE II ATDMA project under a CEC Fellow-ship Contract. Since 1997 he has been withthe University Mediterranea, Reggio Calabria,where he currently holds the position of Headof the Department DIMET. His research

interests include: new generation mobile and wireless systems, broad-band satellite systems, Internet of Things.

Francesco Scarcello received the PhD degreein Computer Science from the University ofCalabria in 1997. He is an associate professorof computer science (SSD ING-INF/05) at theUniversity of Calabria. His research interestsare computational complexity, Game Theory,graph and hypergraph theory, constraint sat-isfaction, logic programming, knowledge rep-resentation, non-monotonic reasoning, anddatabase theory. He has extensively publishedin all these areas in leading conferences andjournals. Professor Scarcello serves on pro-

gram committees and as a reviewer for many international conferencesand journals.

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A fair cooperative content-sharing service

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