AD-SHARE: AN ADVERTISING METHOD IN P2P SYSTEMS BASED ON REPUTATION MANAGEMENT

1 AD-SHARE: AN ADVERTISING METHOD IN P2P SYSTEMS BASED ON REPUTATION MANAGEMENT Nkos Salamanos, Ev Alexogann, Mchals Vazrganns Department of Informatcs, Athens Unversty of Economcs and Busness salaman@aueb.gr, alexogann@yahoo.com, mvazrg@aueb.gr Abstract--We present Ad-Share, a dstrbuted method for mutual advertsement hostng among a group of partcpatng enttes n P2P archtecture. In such archtectures the ssue of free rdng s well known. A multtude of reputaton and ncentve-based methods have been proposed to mprove the system performance. Ad-share s based on two reputaton schemes, the reputaton algorthm EgenTrust and a reputaton-based ncentve model. The Ad-Share consttutes a novel approach towards an onlne dstrbuted advertsng method lackng any payment scheme. We evaluate Ad-Share extensvely n envronment n whch a group of partcpatng organzatons s heterogeneous wth regard to ther qualty and servces and we show that our method can effectvely provde far and robust advertsements assgnments. Index Terms-- Peer-to-Peer, Onlne advertsng, Incentves, Reputaton Management. I. INTRODUCTION Peer-to-peer (P2P) networks are dstrbuted systems that allow the drect communcaton of partcpatng peers wthout the necessary medaton of a server. An extensve survey on P2P networks can be found n [1]. The man characterstc of P2P networks s the absence of central control over the users. The users are autonomous, havng control of ther fles and connect/dsconnect to the network spontaneously. In P2P networks emerge the problem of free rdng. The users manly act as consumers and lack motvaton to contrbute. Extensve research has been conducted n ths area and many models have been proposed to motvate the users contrbutons. The research s focused on applcatons of reputaton and ncentve-based mechansms n P2P networks. A comprehensve survey on onlne reputaton mechansms s [4] and on P2P reputaton systems s [5]. Recallng from [5] the core of any P2P reputaton system s n the answer to the followng queston: how can a gven peer use the experences between the peers, that t can retreve from the network, to evaluate the trustworthness of any other peer? In P2P systems there s no central authorty to dstrbute the reputaton values of the users. Thus there s the necessty for a dstrbuted mechansm to spread the reputaton ratngs for the enttes. In [8] the authors propose a dstrbuted reputaton algorthm that produces global reputaton ratngs for the evaluaton of peers, robust to malcous peers. The reputaton problem n P2P has been studed extensvely usng game theoretc framework and many models have been proposed. Game theory s an approprate tool for modelng systems wth selfsh and autonomous partcpatng enttes. The noton of Nash Equlbrum s a tool for prescrbng of peers behavor. The man underlne assumpton on the behavor of the partcpatng enttes s that are ratonal.e. they act as to maxmze ther proft. Proposed approaches are the mcro- payment model [9], dfferental servce-based ncentve scheme [2]

2 and reputaton-based ncentve model [10]. The recent growth of onlne markets s mpressve and has become the key pont for the companes n the web. A sgnfcant number of frms, from small busnesses to multnatonal corporatons, ncorporate onlne advertsng nto ther marketng strategy. A large number of onlne advertsng methods have been developed, some of the most popular follow: banner ads, emal marketng and search engne marketng. The onlne methods use dfferent types of payment schemes, the most common beng the CPA (Cost Per Acton), the CPC (Cost Per Clck) and the CPV (Cost Per Vstor). In onlne advertsng the scheme s centralzed,.e. there s a servce provder who defnes places on the relevant web server pages to be occuped by the advertsees, e. the enttes that want to be advertsed. The P2P systems have be become very popular manly as fle sharng systems. In ths paper, we deal wth the problem of desgnng a dstrbuted advertsng method for P2P systems lackng any payment scheme. The methods have to be robust and far wth regard to advertsements assgnments. We propose an onlne dstrbuted advertsng method whch allevates the need for a payment mechansm. Our method s decentralzed n the sense that there s not central authorty responsble for the advertsements (ads) assgnments but the companes themselves. Our method s a frst approach for the desgnng a P2P ncentve-based advertsng mechansm. We apply two reputaton mechansms, an ncentve-based scheme [10] and the EgenTrust algorthm [11]. We consder a settng where the partcpatng organzatons (peers) dffer wth regard to ther qualty and servces. We have developed two varatons of the EgenTrust, the frst, group the peers nto homogenous clusters accordng to ther reputaton n real market and the second ensure the homogenety of the clusters. Our proposed method effcently acheves the desred goals of far and robust advertsements assgnments. The paper s organzed as follows. Secton II covers the background of the present method. In Secton III, we present the advertsng method. In Secton IV we present the evaluaton of the method. Fnally, n Secton V we present the conclusons of the paper. II. BACKGROUND In ths secton we revew reputaton models the methods we explot n our advertsng method. The authors n [11] present EgenTrust a dstrbuted reputaton algorthm. EgenTrust evaluates the peers transactons and s based on the noton of transtve trust. Moreover, the algorthm aggregates the reputaton values based on a dstrbuted method robust to malcous peers. In [10] a reputaton model s defned based on ncentves n order to address the problem of free rdng. In the followng we present Egentrust and the ncentve-based model n detal as they are used as an ntegral part of our approach. A. The EgenTrust Algorthm The Egentrust algorthm [11] s based on the noton of transtve trust. Recallng from [11], every peer assgns local trust values to the peers that have commtted at least one transacton n the past. If peer wants to rate unknown peers then t asks ts acquantances about ther opnon about those peers. Acquantances of peer are peers whch peer has rated wth hgh trust value n the past.. When peer rates a transacton wth peer j as postve, then tr 1 (f negatve then tr 1). The local trust value s that peer assgns to peer j s the sum of j = j = j

3 the respectve ratngs, sj = trj. The normalzed local trust value cj s defned as: c j max(s j,0) =. When max(s,0) j j peer rates an unknown peer k, t asks ts acquantances about ther opnon about k. Peer weghts ther opnon ( c jk ) by the trust values ( cj ) t has assgned n them, thus: tk = cj cjk. If C s the matrx [c j] and c a vector contanng the trust values whch assgns to hs acquantances then j T t = C c. If peer ams at mprovng ts knowledge about a larger part of the network t may ask the frends of ts frend s frends and so on. Then, after n T steps we have t = C c. As demonstrated n [11] when n s large the trust vector converges to the (k+ 1) T k vector t = C t. ( ) n In Egentrust the noton of pre-trusted peers s defned as a tool to avod manpulaton from malcous peers. The set P of pre-trusted peers s a subset of the set of peers and they are consdered as honest from the begnnng of the procedure. The noton of pre-trusted peer s mportant for the convergence of the algorthm. The pre-trust value for peer s defned as: 1/ P f P p = (1). Fnally, we have (k+ 1) T k t = ( 1 b) C t + bp, 0 < b<1, where 0 otherwse the parameter b s a constant. In fact each peer computes ts global trust value as follows: k 1 k k k 1 1 2 2 n n t + = (1 b) (c t + c t +... + c t ) + b p (2). The dstrbuted EgenTrust algorthm s defned as follows: For each peer two sets of peers are defned, A : The set of peers that have at least one transacton wth. B : The set of peers wth whch peer has at least one transacton. Then the EgenTrust algorthm appears n Table I. TABLE I THE EIGENTRUST ALGORITHM Each peer do { 0 j Query all peers j A for t = p ; repeat Compute t k+ 1 = (1 b) (c t k +... + c t k ) + b p ; 1 1 n n k 1 Send ct + to all peers j B ; j j t Compute k+ 1 k δ= t t ; Wat for all peers j A to return k 1 ct + j j ; untl δ<ε }

4 B. A Reputaton based Incentve Model The authors n [10] present an ncentve-based scheme n P2P networks to mprove the system performance. They apply a game theoretc model, an nfnte repeated game, analyzng the ncentve scheme and dentfyng the pure and mxed Nash Equlbra. The peer nteractons are modeled as an nfnte repeated game, the Servce Game Tme s dvded n nfnte tme perods. In each of them each peer can has two actvtes; to serve others, to obtan servce for tself. Peers are motvated to serve others by mposng that every peer wll receve servce wth probablty equal to ts current reputaton. Peers gan reputaton only by servng others. The reputaton of each peer s measured each tme perod usng a recursve functon R. The value tme perod t. Functon R t s a lnear functon of the reputaton value R t G. s the reputaton value of a peer n the R t 1and the reputaton value that peer gans from ts actons n perod t. In every tme perod each peer wll ncrease (decrease) ts reputaton value R dependng on ts actons. The request from a peer, n a tme perod t, wll be served from a peer j wth probablty tme perod, each peer receves one request for servce whle t could receve servce one tme per tme perod. R t. In each The ncentve scheme s evaluated usng a game theoretc framework. A servce game nfnte repeated game and s defned as follows: Tme t s dvded nto nfnte tme-perods, t = 0,1,2,,. Each of the N peers s consdered as a player. The set of possble actons for each peer s {Serve, Don t serve} { } t t 1 Functon R s defned as: R = (1 α) R +α ω t 2 (3). G s ntated as an 0 Whle: R = 0, and R =ω,. 1 Parameter ω s set to 1 f the peer chose the acton serve, 0 otherwse. Parameter α, ( 0 α 1) defnes the porton of the reputaton a peer mantans from ts past performance vs. ts current acton. Low values for α mply small changes to a player s reputaton f t does not serve. Basc assumpton s that the populaton of peers s homogeneous.e. have equvalent capabltes and then s dffcult for them to coordnate. The authors n [10] estmate the pure Nash equlbrum and the symmetrc mxed Nash equlbrum of the servce game. They prove that the pure Nash equlbrum s the acton don t serve and a symmetrc mxed Nash Equlbrum s the mxed strategy (p, 1-p), same for all peers. Brefly, the proof s as follows. Accordng to Nash Folk theorem for the nfnte repeated games [12], G and the nfnte repeated game have the same Nash Equlbra. Therefore, we have only to detect the Nash Equlbra of the G. The pure Nash equlbrum of the advertsng game s the acton don t serve. We notce that f a player chooses the acton serve ts payoff s -C nstead of zero n the case t chose the not advertse acton. The payoff of a player who chooses to advertse s C because all the other players wll chose the equlbrum acton and wll not advertse. Ths mples that each player s request wll be rejected. Ths pure equlbrum s unstable, because f the players stay at the equlbrum then the system collapses. For the mxed strategy Nash equlbrum, we notce the game G exhbts a symmetrc Nash equlbrum because G

5 of the homogenety of the peers. The peers are ndfferent about the peer that they wll request for servce. We recall the followng statements from [12]: (Mxed strategy equlbrum exstence) Every fnte strategc game has a mxed strategy Nash equlbrum. Every acton n the support of any player s equlbrum mxed strategy yelds that player the same payoff. The proof s based on these statements and the exstence of a symmetrc mxed Nash Equlbrum. Assume that the symmetrc equlbrum s {p, 1-p} where p s the probablty that the player choose the acton serve. Then: payoff = payoff Serve Don't serve don 't R t p( C + R t U) = (1 p)( R t U) p = (4) C + serve don 't Rt + Rt U If we assume that C don 't 1 U, then R t p = serve don 't R + R rve don 't t t If the functon R s postve and se R t > R t, then regardless of the relaton R t and R t, p s always less than 0,5. Fnally, from (3) and (4) follows: don 't serve don 't t 1 (1 α)r p = C 2(1 α )R t 1+α U (5). Ths s the symmetrc Nash equlbrum for the game G. Also, ths s a stable Nash equlbrum. An mportant observaton s that even we assume C 1 the parameter α must be small n order to the probablty p to converge U to 0,5. III. THE ADVERTISING METHOD We develop an advertsng method for mutual advertsement hostng n a group of partcpatng companes, where each company owns a web ste. We assume that the frms have been clustered n semantcally coherent groups accordng to ther servces and products classfcaton. These semantcally related peers-companes are grouped nto a semantc overlay network (SON). The authors n [3] and [6] show that fles shared n P2P networks can be clustered effcently by content categores. The exact method for the generaton of the semantc overlay network s out of the scope of ths paper. The semantc overlay network contans M semantc categores and each of them L subcategores. In each category peers are evaluated wth regard to the qualty of ther servces and products and are grouped nto relevant qualty categores. The advertsng process starts at each semantc category of SON and at each qualty category ndependently. The basc assumpton s that f the peers n a qualty category are relevant wth regard to reputaton level n the market, then they don t have the motvaton to cooperate. Ths assumpton s mportant for the game theoretc analyss of Ad-share. The Ad-method s based on the combnaton of two reputaton methods: the Egentrust algorthm [11], and an ncentve-based scheme [10], amng to motvate the peers to accept advertsements at ther web stes. Each peer has

6 a dual role, act as advertser (.e. host advertsements on ts web ste) and as advertsee ( pay for havng an advertsement hosted). We have developed two versons of the EgenTrust algorthm, the Egen-Clusterng and Egen-Test. The frst verson computes the reputaton of the companes n the market. Egen-Clusterng clusters the peers n qualty categores accordng to ther reputaton. The underlyng assumpton s that Egen-Clusterng values reflect the reputaton of a company n the market. We cluster the peers n qualty categores n order to ensure that each category has a homogenous populaton of companes. The second verson of EgenTrust, the Egen-Test, s used perodcally, evaluatng the homogenety of the categores. The algorthm ensures that the peers partcpate n a group of companes wtch s homogenous wth regard to reputaton level n the market. Brefly the steps of the method are as follows: After the end of Egen-Clusterng the man advertsng process starts n every qualty category ndependently. The tme s modeled by an nfnte number of advertsng perods (Ad-perods). In each Ad-perod, every peer has a reputaton value Φ. The reputaton values are measured by a recursve functon Φ t. The reputaton values are ncreased each tme the peer acts as advertser. We apply an ncentve n order to motvate the peers to act as advertser. The ncentve s that the request of peer as advertsee (.e. askng for some other peer to host ts advertsement) wll be served wth a probablty equal to ts reputaton value. In the next sectons we descrbe analytcally the stages of the advertsng method. A. The Advertsng Game Smlarly to the servce game G presented n [10] we defne the advertsng game Ad-Game. We assume nfnte consecutve advertsng perods. In every perod each peer has to decde f t wll make avalable for advertsement K slots (at ts webste) or not. The acton open K slots mples that the peer s wllng to accept to host exactly K- ads n ts web ste. We also assume that the peers are honest wth ther choces,.e. f they have opened k slots they would not reject any request for advertsng f they have at least one slot vacant. The underlyng assumpton s that we dentfy the acton of open K-slots wth the potental acceptance at the future K requests for ads hostng. We compute the reputaton values of a peer wth a recursve functon Φ, whose values depend on the actons of a peer. In our model the acton open k slots s equvalent to the acton, advertse K peers. The functon Φt s the functon R (3) usng dfferent ntalzaton strategy. In the same manner as n the servce game n secton II, by default, the probablty for a peer to be advertsed n a web ste s equal to ts reputaton. Under ths ncentve scheme, the peers have the motvaton to be advertsers n order to ncrease ther reputaton and thus to ncrease ther chances of havng thers ads accepted n other peers. We apply a game theoretc approach analyzng the ncentve scheme and dentfyng the pure and mxed Nash Equlbra of the game. We defne the Ad-Game an nfnte repeated game as follows: 1. The tme t s dvded n nfnte ad-perods, t = 1, 2,3...,. 2. We defne the game G. 3. The Ad-Game based on the nfnte repettons of the G. 4. The set of N players s the set of N peers. 5. The set of actons A = {a,a }, for each peer s: 1 2

7 {Open K slots, Don t open K slots} {Advertse K peers, Don t advertse}. 6. We defne the functon Φ as follows: (1 α) Φ t 1+α ω t 1 Φ t = (6). 1 t=0 The N players have to decde ndependently f they are wllng to accept to host K ads n ther webste. Each player/peer represents a company wth a web server. Durng the frst perod all peers have a reputaton value 1. Ths s a dfferent ntalzaton strategy to the one presented n [10]. We gve a bonus of reputaton to every peer at the begnnng of the game n order to have a successful Ad-Hostng from the frst perod. Parameter ω s set to 1 when the player opens Κ slots and 0 otherwse. Followng an analyss smlar to [10] we can detect the Nash Equlbra of the Ad-Game. The pure Nash equlbrum of the advertsng game s the acton {Don t open k slots}. The proof for the symmetrc mxed Nash equlbrum s the same wth the proof for the servce game G n secton II, snce we assume that the group of companes s homogenous. It s easy to prove that the symmetrc mxed Nash equlbrum for the Ad-Game s the strategy (p, 1-p) where: t 1 (1 α) Φ p = C 2(1 α) Φ t 1+α U (7). B. The Egen-Clusterng and Egen Test Algorthms The Ad-method uses two versons of EgenTrust algorthm. The frst verson, Egen-Clusterng, clusters peers n qualty categores Low, Medum and Hgh. Each peer s a company wth a web ste. We assume the peers market reputaton as proportonal to the sze of the company, and the qualty of ts products. Thus the peers partcpatng n the advertsng already know some of the other peers and have an opnon for them. We defne the sets of peer n the same fashon as n the orgnal EgenTrust. Set s the set of peers who have an opnon about. A A and B Set B s the set of peers that peer knows from the market and t can evaluate them (.e. the opnons of peer for the peers t s aware of). We defne the local trust values as the evaluaton of peer to peer j, 0 c 1 wth c = 1,, j. The Egen-Clusterng follows the same approach as EgenTrust appearng n Table- j j B j c j I. We consder all the peers as pre-trusted, P =N, meanng that n the frst repetton of the algorthm each peer has 0 t = 1/ P. The output of the algorthm s the t market values used for the subsequent clusterng. The expermental results show that ths smple measure s effcent for the clusterng process. The second verson, the Egen-Test, evaluates the homogenety of the qualty categores. It runs perodcally at the end of a randomly chosen ad-perod. The algorthm runs smultaneously n all qualty categores of the semantc subcategory. We assume that the peers cannot predct the exact ad-perod durng whch Egen-Test s executed. We choose the ad-perod randomly n order to retan the game theoretc settngs of the nfnte repeated game and to ensure that the equlbrum remans the same. Also, the test can run only after the ad-perod r, where r s the number

8 of perods needed for the recursve functon Φ to converges, and has been defned expermentally. We defne sets A and B and the local trust values c as follows: Assume the Egen-Test runs at the end of the ad-perod µ, then: A µ : The set of peers that peer has advertsed durng the µ Ad-perods. B µ : The set of advertsers of peer durng the µ Ad-perods. j Then, we defne: where: j B µ c j = ν k Bµ j, µ v k, µ (8) ν j, µ : The sum of user clcks on the Ads of peer, wth j as advertser, durng the µ Ad-perods. v : The sum of user clcks on the Ads of peer. k Bµ k, µ The entty c j s the evaluaton of peer to ts advertser peer j, wth regards to the overall advertsng proft that peer receved durng the µ Ad-perods. The dstrbuton of the global Egen-Test values n a qualty category reflects the reputaton level of peers as advertsers. If the Egentrust values dd not exhbt sgnfcant dfferences then we can assume that the qualty category s homogeneous,.e. peers are smlar wth respect to ther reputaton/performance as advertsers. If not, then the peers must be clustered anew, based on the Egen-Test values n all qualty categores. C. The Ad-Share Algorthm Summarly we present the overall steps of the Ad-Share method as execute n each semantc category of a SON. Semantc Overlay Generaton Algorthm 1. Semantcally related peers are grouped nto SON. 2. {< peer d, name of the company, url, Category, SubCategory > 1,..,< > N } denotes the set of peers n a Semantc Category. 3. In each Semantc Category the Egen-Clusterng run. Egen-Clusterng 1. The peers are clustered n qualty categores Low, Medum, Hgh 2. In every qualty category the Ad-hostng process run. Ad-Hostng In every ad-perod: 1. Each peer do 2. Compute probablty p, usng (7) 3. Decde, wth probablty p, opens K- slots or Don t open K-slots

9 4. Compute Φ. 5. Propagate L requests for ad-hostng, where L K. 6. Every request has the form: <peer d, name of the company, url, peer s semantc subcategory, host semantc subcategores (or all ), Φ>. 7. Receve requests for Ad-hostng. A request from a peer j would be served wth probablty Φ j only f : peer has empty slots and peer j s not n the same subcategory wth peer. 8. Store the user-clcks of ads. 9. The Egen-Test run (n a randomly chosen perod) n each qualty category and after the end of perod r. Egen-Test 1. If the Egen-Test run at perod t. 2. Compute the Egen-Test values based on user-clcks from the t perods. 3. Compare the Egen-Test values n each qualty category. 4. If are homogenous, 5. Ad-Hostng run n perod t+1 6. If not, 7. End of Ad-Hostng. 8. Cluster anew n qualty categores all the peers n the semantc category based on Egen-Test values. IV. EVALUATION OF THE METHOD In ths secton we present the expermental results evaluatng the Ad-method. A. Intal Clusterng Frst, we assess the Egen-Clusterng. We smulate each semantc category wth a homogenous network (.e. all nodes have the same connectvty) of 200 peers usng the GTITM topology. As we have already mentoned, the acton open K-slots mples that the peer s wllng to accept to host K-ads and we assume that the peers are honest wth ther choces. We make a smlar assumpton consderng all the peers as pre-trusted. We defne the sets A and B of a peers as the 10% of the peers usng a unform dstrbuton. We defne cj = 1,, j and each peer has to gve a reputaton value to each peer n B. We defne the local trust j B values representng the trust a peer attrbutes to the peers n B - as follows: Assume peer has to evaluate four peers: k, l, m, n, then we choose randomly 3 values between 0 and 1, e.g. 0.156, 0,627, 0.256. We dvde the range (0,1) nto the ntervals (0, 0.156), (0.156, 0.256), (0.256, 0.627), (0.627, 1). The sze of each nterval represents the trust values c, c, c and c. k l m n Then, we estmate the convergence of the Egen-Clusterng for 200 peers, we set b=0.1 n the equaton 2. In Fg. 1(a) we present the Egen-Clusterng values for 20 randomly selected peers and for 10 teraton of the algorthm. Fg.1(b) shows an estmaton of the convergence rate of the Egen-Clusterng, t convergences fast, after the 6 th teraton, smlar wth the orgnal EgenTrust [11].

10 Fg. 1. (a) The Egen-Clusterng values for 20 random peers. b) Egen-Clusterng convergence We further estmate the qualty categores Low, Medum, Hgh for a semantc category from the frequency of the Egen Values for teraton after the convergence of the algorthm. Fg. 2. The frequency dstrbuton of Egen-Clusterng values after the 6 th teraton and for 200 peers. We compute the number of peers wth Egen-Clusterng values n the ntervals [0, 0.001),, [0.009, 0.01] respectvely. The results n Fg. 2 show the frequency dstrbuton of the Egen values. Small number of peers has Egen-Clusterng values nto the nterval [0,002, 0,004) and (0,006, 0,009], those set of peers are the clusters Low and Hgh. More than 50% of peers are drawn to the nterval [0.004, 0.006] and consttute the cluster Medum. Fnally, we defne the qualty categores Low, Medum and Hgh as the sets of peers wth Egen-Clusterng values n the ntervals [0,002, 0.004), [0.004, 0.006] and (0.006, 0.09] respectvely. B. Ad-Hostng The experments n ths secton address the convergence of functon Φ for dfferent values of α. We smulate an unstructured homogenous network wth 200 peers and an average connectvty 4. Each semantc category ncludes 10 subcategores, we assgn the peers to sub categores randomly usng the unform dstrbuton. In every ad-perod the peers choose to advertse others wth probablty p, accordng to mxed Nash Equlbrum (7). In (7) we set C U = 1 100. Each peer has to decde ndependently wth probablty p f t wll open K-slots, wth K=4. In every ad-perod every peer could request for advertsements. The maxmum number of request per peer s K. The requests have the form: <peer s d, name of the company, url, peer s semantc subcategory, host semantc subcategores (or

11 all ), Φ>. At the feld Host sub categores we set all,.e. the peers are ndfferent about the subcategory of ther advertsers. The requests are propagated usng a verson of the m-random walks [8] method as follows: The request s propagated to m randomly chosen neghbours of the peer. Thus, m random paths-requests are created. Each neghbour propagates the request to only one randomly chosen neghbour. The process contnues untl the tme to lve (TTL) of the request reaches zero. If a request s served from a peer then all the others m-1 sub-requests stopped. Ths ensures than every request would be served from one peer. For our smulaton experment we set TTL=10 and we mplement a 4-random walks algorthm. Fg. 3. (a) Average Φ values for 200 peers for varous α. (b) Devaton of Φ for α=0.05 and α=0.1. Fg. 3 depcts the convergence of functon Φ for dfferent values of α. If α > 0,1 Φ convergences to zero. We study further the devaton of Φ, for α=0,1 and 0,05 (Fg. 5). For small values of α the reputaton values converge to 0,5. The next experment computes the average p value and the devaton for 500 Ad-perods and α=0,05 and 0,1 (Fg. 4, 5). Fg. 4. Average p for α=0.05 and α=0.1. Fg. 4 shows that for α=0,05 the probablty p converges very close to 0,5. We recall that the upper bound of p s 0,5. In Fg. 5 we present the devaton of p for α=0,1 and 0,05. The devaton of p for α=0,05 s very small, less than 0,01. Thus, for the rest of the experments we set α=0,05. In the followng experments we estmate the average number of Ads per advertser and the average number of Ads per advertsee. The number of Ads per advertser s very mportant for the effcency of the method snce we want to ensure that the sources of the system (the open slots) wll not reman unused.

12 Fg. 5 Devaton of p for α=0.05 and α=0.1 As can be seen from Fg. 6 the average number of Ads for the advertsers s almost 4 from the frst ad-perod. Ths mples that the peers who are wllng to accept to host K-Ads they host eventually almost 4 Ads per ad-perod. Fg.6. Average number of Ads for the advertsers In Fg. 7(a) and (b) we present the average number of Ads for the advertsees (500 ad-perods) and the devaton. The average number of Ads s sgnfcant of the effcency of Ad-method. The method must ensure that the partcpatng enttes eventually wll be advertsed at every ad-perod. The expermental results shows that n every ad-perod each peers wll be advertsed at least n one web ste. Fg. 7. (a) Average number of Ads for the advertsees. (b) Devaton of Ads for the advertsees. C. Homogenety of clusters In the last secton we assess the performance of Egen-Test. The Egen-Test algorthm runs after µ Ad-perods, where µ randomly chosen, and after Φ has converged. We mplement the same smulaton network as n secton IV- B. We set the followng values for the nvolved parameters: α=0,05, b=0,1 and 0,5. We set α=0,05 because for

13 α=0,05 the probablty p converges very close to 0,5. Also we experment wth b=0,1 and 0,5. The parameter b (2) determnes the percentage of the pre-trust value of peer n an teraton of EgenTrust. We defne the overall qualty of a category as proportonal to the total number of clcks ts advertsements collected n one Ad-perod. We evaluated the Egen-Test for a qualty category of 10.000 user-clcks. We assume that the advertsements n the category are equvalent wth respect to ther penetraton to the market,.e. they gather smlar amounts of user clcks. We assgn the clcks to the advertsements unformly as follows; each advertsement gans a clck wth probablty 1/Y, where Y s the total number of advertsements. Fg. 8(a) shows that the Egen-Test converges after the 6 th teraton. The result s smlar wth those for the convergence of Egen-Clusterng and EgenTrust. Fgures 8(b), 9(a) and 9(b) depct the frequency dstrbuton of Egen-Test values for 50, 100 and 200 ad-perods, assumng b=0,1. Fg. 8. (α) Egen-Test convergence. (b) The frequency dstrbuton of Egen values (b=0,1) We observe that as the number of ad-perods (parameter µ) ncreases the Egen-Test values tend to concentrate n the nterval [0.004, 0.006]. As µ ncreases the sets Α µ and Β µ of the peers grow larger. Thus, the peers evaluate a larger part of the network and the global Egen-Test values tend to concentrate n the same nterval. Fg.9. The frequency dstrbuton of Egen values for 100 and 200 Ad-perods respectvely (b=0,1). We experment wth b=0,5 and the man observaton s that the Egen-Test values tend to the concentrate nto the same ntervals as for b=0,1 but n a much smaller number of perods. Fg. 10(a) and (b) shows the expermental results for b=0,5.

14 Fg.10. The Egen-Test values dstrbuton, for b=0,5, are drawn faster to the same ntervals. V. CONCLUSION In ths paper we have proposed a dstrbuted onlne advertsng method for P2P systems. Our method based on two varatons of EgenTrust algorthm and an ncentve-based scheme. The contrbuton of our method s that t consttutes a novel approach towards an onlne dstrbuted advertsng method lackng any payment scheme. We evaluate the method extensvely and the expermental results show that Ad-Share can effectvely provde far and robust advertsements assgnments. REFERENCES [1] Androutsells - Theotoks S. and Spnells D, A Survey of Peer-to-Peer Content Dstrbuton Technologes, ACM Computng Surveys, Vol. 36, No. 4, December 2004, pp. 335 371. [2] C. Buragohan, D. Agrawal, S. Sur. A Game Theoretc Framework for Incentves n P2P Systems. In Proc. of the Thrd Internatonal Conference on Peer-to-Peer Computng (P2P 03), 2003. [3] A. Crespo and H. Garca-Molna. Semantc Overlay Networks for P2P Systems. Techncal report, Stanford Unversty, 2002. [4] C. Dellarocas. Reputaton Mechansms, n Handbook on Informaton Systems and Economcs, T. Hendershott (ed.), Elsever Publshng, forthcomng, 2006 [5] Despotovc, Z. and Aberer, K., 2004, Possbltes for Managng Trust n P2P Networks. Swss Federal Insttute of Technology (EPFL) Techncal Report IC/2004/84, Lausanne, Swtzerland. [6] Doulkerds Chrstos, Norvag Kjetl and Vazrganns Mchals, DESENT: Decentralzed and Dstrbuted Semantc Overlay Generaton n P2P Networks, IEEE Journal On Selected Areas In Communcatons, Vol. 25, No. 1, January 2007 [7] Feldman Mchal and Chuang John, Overcomng Free-Rdng Behavor n Peer-to-Peer Systems, ACM SIGecom Exchanges, Vol. 5, No. 4, July 2005, Pages 41-50 [8] C. Gkantsds, M. Mhal, A. Saber, RandomWalks n P2P Networks, IEEE INFOCOM 04, HK, Mar.2004. [9] P. Golle, K. Leyton-Brown, I. Mronov, and M. Lllbrdge. Incentves for sharng n peer-to-peer networks. In Proc. of 2001 ACM Conference on Electronc Commerce, 2001 [10] Gupta R. and Soman A. K., Game Theory As A Tool To Strategze As Well As Predct Nodes' Behavor In Peer-to-Peer Networks, Proceedngs of the 2005 11th Internatonal Conference on Parallel and Dstrbuted Systems (ICPADS'05). [11] Kamvar S. D., Schlosser M. T. and Garca-Molna H., The EgenTrust Algorthm for Reputaton Management n P2P Networks, WWW2003, May 20 24, 2003, Budapest, Hungary [12] Osborne M. J., A Course n game theory, Cambrdge, Mass.: MIT Press