Bayesian Network-Based Trust Model

Transcription

1 Bayesian Network-Based Trust Model Yao Wang, Julita Vassileva University of Saskatchewan, Computer Science Department, Saskatoon, Saskatchewan, S7N 5A9, Canada {yaw181, Abstract We review trust and reputation mechanisms applied in centralized and decentralized systems. Then we propose a Bayesian network-based trust model. Since trust is multi-faceted, even in e same context, agents still need to develop differentiated trust in different aspects of oer agents behaviors. The agent s needs are different in different situations. Depending on e situation, an agent may need to consider its trust in a specific aspect of anoer agent s capability or in a combination of multiple aspects. Bayesian networks provide a flexible meod to present differentiated trust and combine different aspects of trust. A Bayesian network-based trust model is presented for a file sharing peer-to-peer application. 1. Introduction Large distributed systems applied in e areas of e- commerce, web-services, distributed computing, and file sharing peer-to-peer (pp) systems, consist of autonomous and heterogeneous agents, which behave on e behalf of users. Usually, agents play two roles, e role of service providers (sellers, servers) and e role of consumers (buyers, clients). Since agents are heterogeneous, some agents might be benevolent and provide high-quality services, oers might be buggy and unable to provide highquality services, and some might be even malicious by providing bad services or harming e consumers. Since ere is no centralized node to serve as an auority to supervise agents behaviors and punish agents at behave badly, malicious agents have an incentive to harm oer agents to get more benefit because ey can get away. Some traditional security techniques, such as service providers requiring access auorization, or consumers requiring server auentication, are used as protection from known malicious agents. However, ey cannot prevent from agents providing variable-quality service, or agents at are unknown. Mechanisms for trust and reputation can be used to help agents distinguish good from bad partners. This paper describes a trust and reputation mechanism at allows agents to discover partners who meet eir individual requirements, rough individual experience and sharing experiences wi oer agents wi similar preferences. The rest of is paper is organized as follows: section discusses some related issues about trust and reputation. Section 3 introduces our approach to developing a Bayesian network-based trust model. The experiment design and results are presented in Sections 4 and 5. Section 6 discusses related work on trust and reputation. In e last section, we present conclusions and directions for future work.. Trust and Reputation Trust and reputation mechanisms have been proposed for large open environments in e-commerce, distributed computing, recommender systems. Agents are often used to manage and reason about trust and reputation. In is situation, trust is defined as an agent s belief in attributes such as reliability, honesty and competence of e trusted agent. The reputation of an agent defines an expectation about its behavior, which is based on oer agents observations or information about e agent s past behavior wiin a specific context at a given time. Suppose ere are two agents, agent A and agent B. When agent A has no direct interaction wi agent B or it is not sure about e trustworiness of B, agent A can make decisions relying on e reputation of agent B (obtained rough asking oer agents). Once agent A has interactions wi agent B, it can develop its trust in agent B according to its degree of satisfaction wi e interactions and use is trust to make decisions for future interactions. Some of e literature on trust and reputation treats e two concepts interchangeably or ambiguously, which sometimes causes confusion [1, 16]. The two concepts are related, but different. Agent A s trust in agent B is e accumulation of evaluations at agent A has of its past interactions wi B. It reflects agent A s subjective viewpoint of B s capability. The reputation of agent B is an objective measure for agent B s capability, resulting from e evaluations of many oer agents. There are two ways for agent A to learn agent B s reputation. One is to ask an auority, like a better business bureau, which is responsible for accumulating evaluations of agents (including B) from oer agents and calculating e reputation of e evaluated agents (e.g. B) based on ese evaluations. In is case, e auority usually does not care who provides an evaluation, an honest agent or dishonest agent, but relies on e amount of data to make e effect of possible biased evaluations in-

2 significant. Centralized systems, such as ebay and onsale, use is way of building reputation. The oer way for A to obtain agent B s reputation is to proactively request and collect oer agents evaluations about B and to combine e evaluations togeer to form its own view of B reputation. This way of computing reputation is adopted in decentralized systems [5]. Trust can be broadly categorized by e relationships between e two involved agents in e following categories [7]. Trust between a user and her agent(s). Alough an agent behaves on its user s behalf, an agent might not act as its user expects. How much a user trusts her agent determines how she delegates her tasks to e agent [18]. Trust in service providers. It measures wheer a service provider can provide trustwory services. Trust in references. References refer to e agents at make recommendations or share eir trust values. It measures wheer an agent can provide reliable recommendations. Trust in groups. It is e trust at one agent has in a group of oer agents. By modeling trust in different groups, an agent can decide to join a group at can bring it most benefit [19]. Hales [8] points at group reputation can be a powerful mechanism for e promotion of beneficent norms under e right condition. This kind of trust is also useful in helping an agent judge e oer agent according to its trust in e group at e oer agent belongs to [6, 8, 1, 19]..1 Centralized vs. Decentralized Trust and reputation mechanisms have been implemented in many systems adopting eier a centralized structure or a decentralized structure. Accordingly, e trust and reputation mechanisms used in e two kinds of systems are also different. In centralized systems, such as in ebay and onsale, which are mainly seen in e area of e-commerce, e trust and reputation mechanisms used are relatively simple. There are some common characteristics in ese systems. A centralized node acts as e system manager responsible for collecting ratings from bo sides involved in an interaction. Agents reputations are public and global. The reputation of an agent is visible to all e oer agents. Agents reputations are built by e system. There is no explicit trust model between agents. Less communication is required between agents. An agent only communicates wi e centralized node to know oer agents reputations. Despite of e simplicity of e centralized reputation, empirical results show ese systems do encourage transactions between sells and buyers. But ere are some problems. Agents are usually reluctant to give negative ratings because ey can see each oer s ratings and are afraid of revenges [15]. Anoer problem is at if an agent has a bad reputation, it can discard its old identity, choose a new one, start as a beginner and get rid of its poor reputation. The ird problem is at agents can increase eir reputations artificially by creating fake identities and having em to give emselves high ratings [4]. The trust and reputation mechanisms used in decentralized systems, for example, peer-to-peer networks, are more complex an ose applied in centralized systems. They have e following characteristics [, 3, 5]: There is no centralized system manager to govern trust and reputation. Subjective trust is explicitly developed by each agent. Each agent is responsible for developing its own trust in oer agents based on eir direct interactions. No global or public reputation exists. If agent A wants to know agent B s reputation, it has to proactively ask oer agents for eir evaluations of B, en synesize e ratings togeer to compute agent B s reputation. The reputation of agent B developed by A is personalized because agent A can choose which agents it will ask for evaluations of B, its trustwory friends or all known agents. Agent A can also decide how to combine e collected evaluations togeer to get agent B s reputation. For example, it can only combine e evaluations coming from trusted agents. Or it can weight differently e evaluations from trusted agents, unknown agents and even untrustwory agents when it combines em togeer. A lot of communication is required between agents to exchange eir evaluations. In decentralized systems, agent A can get agent B s reputation based on its own knowledge of e trufulness of agents at make recommendations for agent B. So it is difficult for agent B to increase its reputation artificially. Since only agent A can see e recommendations, e references can express eir feelings trufully, not worried about potential revenges. But e tradeoff is at agents have to conduct a lot of communication and computation. 3. Bayesian Network-Based Trust Model Most current applications and experiments on trust and reputation only focus on one of em, eier trust or reputation, alough e idea of combining em togeer in one system has been well known in e literature [4, 1,, 3]. An agent broadly builds two kinds of trust in anoer agent. One is e trust in anoer agent s competence in providing services. The oer is e trust in anoer agent s reliability in providing recommendations about oer agents. Here e reliability includes two aspects: wheer e agent is truful in telling its information and wheer e agent is trustwory or not. Since agents are heterogeneous, ey judge oer agent s behaviour by different criteria. If eir criteria are similar, one agent can trust anoer

3 agent. If eir criteria are different, ey cannot trust each oer even if bo of em tell e tru. In e implementation of such a system based on trust and reputation, some issues have to be considered. 1) How does an agent model its user? The user ultimately sets e criteria by which an agent evaluates oer agents. Each user has different preferences and ways of judging e quality of interaction. In order to behave as its user wants, an agent has to keep learning its user s preferences and behaviors. If an agent fails to do as what its user expects, it will be useless. ) How is an interaction to be evaluated? Trust is built based on an agent s direct interactions wi oer agents. For each interaction, an agent s degree of satisfaction of e interaction will directly influence its trust in e oer agent involved in e interaction. Usually, an interaction has multiple aspects and can be judged from different points of view. 3) How does an agent represent and update its trust in anoer agent? 4) When will an agent ask for recommendations about anoer agent at it intends to interact wi? 5) How does an agent combine togeer e recommendations for a given agent coming from different references? Since e recommendations might come from trusted agents, non-trusted agents or strangers, an agent has to decide how to deal wi em. 6) How does an agent decide if anoer agent is trustwory to interact wi or not, according to its direct experiences or from e agent s reputation, or bo? 7) How does an agent develop and update its trust in a reference agent at makes recommendations? 8) How many kinds of trust does an agent need to develop wi anoer agent in a single context? Agents may need to develop multiple trust relationships wi each oer in order to evaluate each oer from different perspectives and take different aspects of e agent s behavior into account. For example, agent A might trust agent B in providing music files wi good quality. But agent A might not trust agent B in offering movie files wi e same quality as music files. Our approach will deal wi all e issues above except e first one, which is beyond our scope, alough it is extremely important. We will use a peer-to-peer file sharing application as an example in e discussion, however e meod is general and can be applied to oer applications, like web-services, e-commerce, recommender systems or peer-to-peer distributed computing. 3.1 Scenario In e area of file sharing in peer-to-peer networks, all e peers are bo providers and users of shared files. Each peer plays two roles, e role of file provider offering files to oer peers and e role of user using files provided by oer peers. In order to distinguish e two roles of each peer, in e rest of paper, when a peer acts as a file provider, we call it file provider; oerwise, we call it simply agent. Agents will develop two kinds of trust, e trust in file providers competence (in providing files) and e trust in oer agents reliability in making recommendations. We assume all e agents are truful in telling eir evaluations. However, e agents may have different ways of evaluating oer agent s performance, which reflect different user preferences. 3. Trust in a File provider s Competence In a peer-to-peer network, file providers capabilities are not uniform. For example, some file providers may be connecting rough a high-speed network, while oers connect rough a slow modem. Some file providers might like music, so ey share a lot of music files. Some may be interested in movies and share more movies. Some may be very picky about file quality, so ey only keep and share files wi high quality. Therefore, e file provider s capability can be presented in various aspects, such as e download speed, file quality and file type (see Figure 1). DS Trust in a FP T FQ FT Download speed File Quality File Type Figure 1. A Bayesian Network Model The agent s needs are also different in different situations. Sometimes, it may want to know e file provider s overall capability. Sometimes it may only be interested in e file provider s capability in some particular aspect. For instance, an agent wants to download a music file from a file provider. At is time, knowing e file provider s capability in providing music files is more valuable for e agent an knowing e file provider s capability in providing movies. Agents also need to develop differentiated trust in file providers capabilities. For example, e agent who wants to download a music file from e file provider cares about wheer e file provider is able to provide a music file wi good quality at a fast speed, which involves e file provider s capabilities in two aspects, quality and speed. How does e agent combine its two separated trusts togeer, e trust in e file provider s capability in providing music files wi good quality and e trust in e file provider s capability in providing a fast download speed, in order to decide if e file provider is trustwory or A not? Bayesian network provides a flexible meod to solve e problem. A Bayesian network is a relationship network at uses statistic meods to represent probability relation-

4 ships between different agents. Its eoretical foundation is e Bayes rule [14]. e h). h) p ( h e) = e) h) is e prior probability of hypoesis h; e) is e prior probability of evidence e; h e) is e probability of h given e; e h) is e probability of e given h. A naïve Bayesian network is a simple Bayesian network. It is composed of a root node and several leaf nodes. We will use a naïve Bayesian network to represent e trust between an agent and a file provider. Every agent develops a naive Bayesian network for each file provider at it has interacted wi. Each Bayesian network has a root node T, which has two values, satisfying and unsatisfying, denoted by 1 and 0, respectively. T=1) represents e value of agent s overall trust in e file provider s competence in providing files. It is e percentage of interactions at are satisfying and measured by e number of satisfying interactions m divided by e total number of interactions n. is e percentage of not satisfying interactions. m p ( = (1) n p ( + = 1 The leaf nodes under e root node represent e file provider s capability in different aspects. Each leaf node is associated wi a conditional probability table (CPT). The node, denoted by FT, represents e set of file types. Suppose it includes five values, Music, Movie, Document, Image and Software. Its CPT is showed in table 1. Each column follows one constraint, which corresponds to one value of e root node. The sum of values of each column is equal to 1. Table 1. The CPT of Node FT T = 1 T = 0 Music p ( FT = " Music" p ( FT = " Music" Movie p ( FT = " Movie" p ( FT = " Movie" Document p ( FT = " Docu" p ( FT = " Docu" Image p ( FT = " Image" p ( FT = " Image" Software p ( FT = " Soft" p ( FT = " Soft" FT = " Music" is e conditional probability wi e condition at an interaction is satisfying. It measures e probability at e file involved in an interaction is a music file, given e interaction is satisfying. It can be computed according to e following formula: FT = " Music", p ( FT = " Music" = p ( FT = " Music", is e probability at interactions are satisfying and files involved are music files. m1 FT = " Music", = n m1 is e number of satisfying interactions when files involved are music files. p ( FT = " Music" denotes e probability at files are music files, given interactions are not satisfying. The probabilities for oer file types in Table 1 are computed in a similar way. Node DS denotes e set of download speeds. It has ree items, Fast, Medium and Slow, each of which covers a range of download speed. Node FQ denotes e set of file qualities. It also has ree items, High, Medium and Low. Its CPT is similar to e one in table 1. Here we only take ree aspects of trust into account. More relevant aspects can be added in e Bayesian network later to account for user preferences wi respect to service. Once getting nodes CPTs in a Bayesian network, an agent can compute e probabilities at e corresponding file provider is trustwory in different aspects by using Bayes rules, such as p ( T = 1 FT = " Music" ) e probability at e file provider is trustwory in providing music files, p ( T = 1 FQ = " High" ) e probability at e file provider is trustwory in providing files wi high quality, p ( T = 1 FT = " Music", FQ = " High" ) e probability at e file provider is trustwory in providing music files wi high quality. Agents can set various conditions according to eir needs. Each probability represents trust in an aspect of e file provider s competence. Wi e Bayesian networks, agents can infer trust in e various aspects at ey need from e corresponding probabilities. That will save agents much effort in building each trust separately, or developing new trust when conditions change. After each interaction, agents update eir corresponding Bayesian networks. 3.3 Evaluation of an Interaction Agents update eir corresponding Bayesian networks after each interaction. If an interaction is satisfying, m and n are bo increased by 1 in formula (1). If it is not satisfying, only n is increased by 1. Two main factors are considered when agents judge an interaction, e degree of eir satisfaction wi e download speed s ds and e degree of eir satisfaction wi e quality of downloaded file s fq. The overall degree of agents satisfaction wi an interaction s is computed as e following: s = w * s + w * s, where w w = 1 () ds ds fq fq ds + fq w ds and w fq denote weights, which indicate e importance of download speed and e importance of file quality to a particular agent (depending on e user s preferences). Each agent has a satisfaction reshold s t. If s < st, e interaction is unsatisfying; oerwise, it is satisfying. 3.4 Handling Oer Agents Recommendations

5 In current file sharing peer-to-peer application, users find files by using e search function. In most of situations, ey get a long list of providers for an identical file. If a user happens to select an unsuitable provider, who provides files wi bad quality or slow download speed, e user will waste time and effort. If is situation happens several times, e users will be frustrated. In order to solve e problem, we use e mechanism of trust and reputation. Once an agent receives a list of file providers for a given search, it can arrange e list according to its trust in ese file providers. Then e agent chooses e most trusted file providers in e top of e list to download files from. If e agent has no experiences wi e file provider, it can ask oer agents to make recommendations for it. The agent can send various recommendation requests according to its needs. For example, if e agent is going to download a movie, it may care about e movie s quality. Anoer agent may care about e speed. So e request can be Does e file provider provide movies wi good qualities? If e agent cares bo about e quality and e download speed, e request will be someing like Does e file provider provide files wi good quality at a fast download speed?. When oer agents receive ese requests, ey will check eir trust-representations, i.e. eir Bayesian networks, to see if ey can answer such questions. If an agent has downloaded movies from e file provider before, it will send recommendation at contains e value p ( T = 1 FT = " Music", FQ = " High") to answer e first request or e value p ( T = 1 FT = " Music", FQ = " High", DS = " Fast") to answer e second request. The agent might receive several such recommendations at e same time, which may come from e trustwory acquaintances, untrustwory acquaintances, or strangers. If e references are untrustwory, e agent can discard eir recommendations immediately. Then e agent needs to combine e recommendations from trustwory references and from unknown references to get e total recommendation for e file provider: r ij k tr * t = w l w z t * = 1 + = 1 k s * g tr l = 1 il il lj g t zj,where w w = 1 (3) t + s rij is e total recommendation value for e j file pro- vider at e i agent gets. k and g are e number of trustwory references and e number of unknown references, respectively. tr il is e trust at e i user has in e l trustwory reference. tlj is e trust at e l trustwory reference has in j file provider. t zj is e trust at e z unknown reference has in j file provider. w t and ws are e weights to indicate how e user values e importance of e recommendation from trustwory references and from unknown references. Since agents often have different preferences and points of view, e agent s trustwory acquaintances are ose agents at share similar preferences and viewpoints wi e agent most of time. The agent should weight e recommendations from its trustwory acquaintances higher an ose recommendations from strangers. Given a reshold θ, if e total recommendation value is greater an θ, e agent will interact wi e file provider; oerwise, not. If e agent interacts wi e file provider, it will not only update its trust in e file provider, i.e. its corresponding Bayesian network, but also update its trust in e agents at provide recommendations by e following reinforcement learning formula: n o trij α * trij + (1 α ) * eα = (4) n tr ij denotes e new trust value at e i agent has in o e j reference after e update; tr denotes e old trust value. α is e learning rate a real number in e interval [0,1]. e α is e new evidence value, which can be -1 or 1. If e value of recommendation is greater an θ and e interaction wi e file provider afterwards is satisfying, e α is equal to 1; in e oer case, since ere is a mismatch between e recommendation and e actual experience wi e file provider, e evidence is negative, so e α is -1. Anoer way to find if an agent is trustwory or not in telling e tru is e comparison between two agents Bayesian networks relevant to an identical file provider. When agents are idle, ey can gossip wi each oer periodically, exchange and compare eir Bayesian networks. This can help em find oer agents who share similar preferences more accurately and faster. After each comparison, e agents will update eir trusts in each oer according e formula: n o tr = β * tr + (1 β ) e (5) ij ij * The result of e comparison e β is a number in e interval [-1, 1]. β is e learning rate a real number in e interval [0,1] which follows e constraint β > α. This is because e Bayesian network collectively reflects an agent s preferences and viewpoints based on all its past interactions wi a specific file provider. Comparing e two agents Bayesian networks is tantamount to comparing all e past interactions of e two agents. The evidence eα in formula (4) is only based on one interaction. The evidence e β should affect e agent s trust in anoer agent more an e α. How do e agents compare eir Bayesian networks and how is e β computed? First, we assume e structures of Bayesian networks of all agents have e same structure. ij β

6 We only compare e values in eir Bayesian networks. Suppose agent 1 will compare its Bayesian network (see Figure 1) wi e corresponding Bayesian network of agent. Agent 1 obtains e degree of similarity between e two Bayesian networks by computing e similarity of each pair of nodes (T, DS, FQ and FT), according to e similarity measure based on Clark s distance [1], and en combining e similarity results of each pair of nodes togeer. 4 eβ = 1 * ( w 1i * ci ), where i= 1 c1 w 11 + w1 + w13 + w14 = 1 (6) ( v111 v11) ( v11 v1 ) + ( v111 + v11) ( v11 + v1 ) = (7) hi ( v1ijl vijl ) ( 1 + ) = 1 = 1 = j v l ijl v ijl c i, where i =, 3, 4 (8) w 1 1, w 1, w 13 and w 14 are e weights of e node T, DS, FQ, and FT, respectively, related to agent 1, which indicate e importance of ese nodes in comparing two Bayesian networks. c 1, c, c 3 and c4 are e results of comparing agent 1 and agent s CPTs about node T, DS, FQ and FT. Since e node T is e root node and it has only one column in its CPT, while oer nodes (DS, FQ, FT) are e leaf nodes and have two columns of values in eirs CPTs, we compute c 1 differently from c, c 3, and c 4. hi denotes e number of values in e corresponding node. h = 3 ; h 3 = 3 ; h 3 = 5. v111 and v11 are e values of and related to agent 1. v11 and v1 are e values of and related to agent. v1 ijl and v ijl are e values in agent 1 s CPTs and agent s CPTs, respectively. The idea of is metric is at agents compute not only eir trust values, eir CPTs, but also take into account eir preferences (encoded as e weights, w 11, w 1, w 13, w 1 4 ). So agents wi similar preferences, such as e importance of file type, quality, download speed, will weight each oer s opinions higher. streng of e agent s interests in e corresponding file type. The files e agent wants to download are generated based on its interest vector. Every agent keeps two lists. One is e agent list at records all e oer agents at e agent has interacted wi and its trust values in ese agents. The oer is e file provider list at records e known file providers and e corresponding Bayesian networks representing e agent s trusts in ese file providers. Each file provider has a capability vector showing its capabilities in different aspects, i.e. providing files wi different types, qualities and download speeds. Our experiments involve 10 different file providers and 40 agents. Each agent will gossip wi oer agents periodically to exchange eir Bayesian networks. The period is 5, which means after each 5 interactions wi oer agents, e agent will gossip once. w ds = w fq = 0.5; α = 0.3; β = 0.5; w 11 = w 1 = w 13 = w 14 = 0.5. The total number of interactions is We run each configuration for 10 times and use e means for e evaluation criteria. 5. Results The goal of e first experiment is to see if a Bayesian network-based trust model helps agents to select file providers at match better eir preferences. Therefore we compare e performance (in terms of percentage of successful recommendations) of a system consisting of agents wi Bayesian network-based trust models and a system consisting of agents (wiout Bayesian networks, BN) at represent general trust, not differentiated to different aspects. Successful recommendations are ose positive recommendations (obtained based on formula 3) when agents are satisfied wi interactions wi recommended file providers. If an agent gets a negative recommendation for a file provider, it will not interact wi e file provider. We have two configurations in is experiment: Trust and reputation system wi BN: e system consists of agents wi Bayesian networks-based trust models at exchange recommendations wi each oer; Trust and reputation system wiout BN: e system consists of agents at exchange recommendations, but don t model differentiated trust in file providers. 4. Experiments In order to evaluate is approach, we developed a simulation of a file sharing system in a peer-to-peer network. The system is developed on e JADE.5. For e sake of simplicity, each node in our system plays only one role at a time, eier e role of file provider or e role of an agent. Every agent only knows oer agents directly connected wi it and a few file providers at e beginning. Every agent has an interest vector. The interest vector is composed of five elements: music, movie, image, document and software. The value of each element indicates e

7 Successful recommendations(%) Trust and reputation system wi BN Trust and reputation System wiout BN The number of Interactions Figure. Trust and Reputation System wi BN vs. Trust and Reputation System wiout BN Figure shows at e system using Bayesian networks performs slightly better an e system wi general trust in terms of e percentage of successful recommendations. Successful interactions(%) Trust and reputation system wi BN Trust and reputation system wiout BN Trust system wi BN Trust system wiout BN The number of interactions Figure 3. The Comparison of Four Systems The goal of e second experiment is to see if exchanging recommendation values wi oer agents helps agents to achieve better performance (defined as e percentage of successful interactions wi file provider). For e reason, we compare four configurations: Trust and reputation system wi BN; Trust and reputation system wiout BN; Trust system wi BN: e system consists of agents wi Bayesian networks-based trust models, which don t exchange recommendations wi each oer; Trust system wiout BN: e system consists of agents at have no differentiated trust models and don t exchange recommendations wi each oer. Figure 3 shows at e two systems, where agents share information wi each oer, outperform e systems, where agents do not share information. The trust system using Bayesian networks is slightly better an e trust system wiout using Bayesian networks. There is an anomaly in e case when agents do not share recommendations, since in e end of e curve, e system wiout BN perform better an e system wi BN. This could be explained wi an imprecise BN due to insufficient experience. In some sense, an agent s Bayesian network can be viewed as e model of a specified file provider from e agent s personal perspective. In our experiments, we use a very simple naïve Bayesian network, which can not represent complex relationships. In e real file-sharing system, e model of file providers might be more complex and required e use of a more complex Bayesian network. Our Bayesian network only involves ree factors. If we build a more complex Bayesian network and add more aspects into it, e system performance might be improved. 6. Discussion and Related work How many Bayesian networks can an agent afford to maintain to represent its trust in oer agents in e networks? It depends on e size of e network and e likelihood at agents have repeated interactions. Resnick [15] empirically shows at 89.0% of all seller-buyer pairs in ebay conducted just one transaction during a five-mon period and 98.9% conducted no more an four. The interactions between e same seller and e same buyer are not repeatable. The buyer s trust in a seller is only based on one direct interaction. The seller s reputation is mostly built on e buyers having a single experience wi e seller. This situation often happens in a very large network or in large e-commence sites. Since ere are a large number of sellers and buyers, e chance at a buyer meets e same seller is rare. But if e kind of goods being transacted is only interesting to a small group of people, for example, collectors of ancient coins, e interactions about is kind of goods happen almost exclusively in a small group. So e probability at sellers and buyers have repeated interactions will be high, and ey will be able to build trust in each oer by our meod. Our approach is useful in situations where two agents can repeatedly interact wi each oer. In a small-size network, ere is no doubt at our approach is applicable. For a large network, our approach is still suitable under e condition at e small-world phenomenon happens. The small-world phenomenon was first discovered in e 1960ies by social scientists. Milgram s experiment showed at people in e U.S. are connected by a short (average leng of 6) chain of intermediate acquaintances. Oer studies have shown at people tend to interact wi oer people in eir small world more frequently an wi people outside. The phenomenon also happens in peer-to-peer networks. Jovanovic s work [9] proves at e smallworld phenomenon occurs in Gnutella. It means at agents are inclined to get files from oer agents from a small sub-

8 community. This small sub-community often consists of agents at have similar preferences and viewpoints. Abdul-Rahman and Hailes [1] capture e most important characteristics of trust and reputation and propose e general structure for developing trust and reputation in a distributed system. Most of e later works in e area follow eir ideas, but in different application domain, such as [3, 5, 11]. Sabater and Sierra s work [16] extends e notion of trust and reputation into social and ontological dimensions. Social dimension means at e reputation of e group at an individual belongs to also influences e reputation of e individual. Ontological dimension means at e reputation of an agent is compositional. The overall reputation is obtained as a result of e combination of e agent s reputation in each aspect. Our approach integrates ese two previous works [1, 16], and applies em to file sharing system in peer-to-peer networks. Anoer difference between our work and Sabater and Sierra s work is at we use Bayesian networks to represent e differentiated trust at different aspects, oer an e structure of ontology. Anoer difference is at we don t treat e differentiated trusts as compositional. Usually e relationship between different aspects of an agent is not just compositional, but complex and correlative. Our approach provides an easy way to present a complex and correlative relationship. Our approach is also flexible in inferring e trust of an agent for different needs. For example, sometimes we care about e overall trust. Sometimes we only need to know e trust in some specific aspect. This bears parallel wi work on distributed user modeling and purpose-based user modeling [13, 0]. Cornelli s work [5], like ours, is in e area of file sharing in peer-to-peer networks. However, it concentrates on how to prevent e attacks to a reputation system and does not discuss how agents model and compute trust and reputation. 7. Conclusions In is paper, we propose a Bayesian network-based trust model. Bayesian networks provide a flexible meod to represent differentiated trust in different aspects of each oer s capability and combine different aspects of trust. We evaluated our approach, in a simulation of a file sharing system in a peer-to-peer network. Our experiments show at e system where agents communicate eir experiences (recommendations) outperforms e system where agents do not communicate wi each oer, and at a differentiated trust adds to e performance. Future work includes adding more aspects in e Bayesian networks, trying to find e key parameters at influence e system performance, and testing e system under oer performance measures, for example, how fast an agent can locate a trustwory service provider. Applying is approach to distributed systems for computational services is particular promising. References [1] Abdul-Rahman A. and Hailes S. Supporting trust in virtual communities. In Proceedings of e Hawai i International Conference on System Sciences, Maui, Jan 000. [] Abdul-Rahman A. and Hailes S. A Distributed Trust Model. In Proceedings of e 1997 New Security Paradigms Workshop, ACM, [3] Azzedin F. and Maheswaran M. Evolving and Managing Trust in Grid Computing Systems. IEEE Canadian Conference on Electrical & Computer Engineering (CCECE '0), May 00. [4] Carter J., Bitting E. and Ghorbani A. Reputation Formalization for An Information-Sharing Multi-Agent System, Computational Intelligence, Volume 18, Number 4, November 00. [5] Cornelli F. and Damiani E. Implementing a Reputation- Aware Gnutella Servent. In Proceedings of e International Workshop on Peer-to-Peer Computing, Pisa, 00. [6] Esfandiari B. and Chandrasekharan S. 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