Software agents can form multidimensional, relationship based networks potentially able to realize not trivial forms of interaction and cooperation among agents. In similar contexts, honest agents could be exposed to malicious behaviors acted by unqualified potential partners. Trust and Reputation Systems are efective tools able to mitigate such risks by providing the agent community with suitably information about the trustworthiness of the potential partners in order to allow a good partner choice. In such a framework, we propose: (i) a method to preliminarily identify the best promising candidates as malicious assigning them the role of pre-untrusted entities and (ii) a novel reputation model capable to accurately identify malicious agents without introducing collateral efects on the reputation scores of honest ones.
malicious behaviors, from simple ones (e.g. selfishness, misjudgment) to more sophisticated ones (e.g. colluding). In addition, in presence of large agent environments, nomadic agents, or other events, the probability of interacting with partners whose trustworthiness is still unknown might increase, in such a way agents will be exposed to greater risks of deceptions. Obviously, minimizing such risks is a main aspect for enhancing social aspect in agent communities.
Trust (i.e. reputation) is a powerful means to achieve this goal and making social interactions more satisfying as possible. Therefore, to minimize risks each agent could be provided with appropriate trust measures about the other agents belonging to the same community in order to improve the probability of interacting with reliable partners or, conversely, deciding of not interacting with anyone.
However, the concept of trust cannot be uniquely defined and measured because it is inlfuenced by measurable and not measurable properties involving multiple dimensions (like competence, honesty, security, reliability, etc.) and depending on the specific situational context under which the interactions between the two agents happen. Due to this multifaceted nature, several meanings have been associated with the term “trust”. From our viewpoint, we have interest in addressing subjectivity and situational risks, two aspects playing a fundamental role in the agent societies. To this purpose, in the following we will define trust as: • “Trust is the subjective probability by which an individual, A, expects that another individual, B, performs a given action on which its welfare depends” [10]; • “Trust is the extent to which one party is willing to depend on something or somebody in a given situation with a feeling of relative security, even though negative consequences are possible” [11].
Trust and Reputation Systems (TRSs) are equipping a great number of applications belonging to a large variety of scenarios [12, 13, 14, 15]. From a practical viewpoint, TRSs are Decision Support Tool because they enable agents’ choices providing them with information about the trustworthiness of their potential partners on the basis of (i) direct information derived by a direct knowledge of the trustor about a trustee and/or (ii) indirect information considering ratings and/or opinions provided by other members of the own community about that trustee. Generally, TRSs represent the agent’s trustworthiness by means of a unique score which can be used to identify dishonest actors from honest ones.
However, a main problem of TRSs in detecting malicious agents is that of adopting computational processes that not penalize the reputation scores of honest agents. Unfortunately, this is not unusual as, for instance, in the well known reputation system EigenTrust [16]. To this aim, our contribution is focused on proposing a novel reputation model, designed for agent-based social communities, which careful preserves the reputation scores of honest agents in detecting malicious ones. Moreover, we developed a technique to preliminarily select the most promising agent candidates to be identified as colluding and using them as pre-untrusted agents.
The rest of the paper is organized as follows. Section 2 introduces some related work. The Section 3 describes the reference agent scenario adopted for our reputation model, presented in Section 4. In Section 5, a case study provides a practical example for our proposed reputation model and, finally, some conclusions and future works are drawn in Section 6.
In social agent communities a relevant issue is represented by recognizing malicious actors [17,
18, 19, 20, 21, 22]). Trust and Reputation Systems (TRSs) provide a defense against cheaters that
might perform various misleading behaviors [
In more detail, Trust Systems (TSs) combine information both direct raising by own past
experiences (i.e. ”reliability”) and indirect given by opinions provided by other members of
the community (i.e. ”reputation”), as in [
Even though it is dificult comparing systems developed for specific scenarios, a number of
studies addressed this issue with respect to a more or less wide range of malicious behaviors.
To this aim, in [
To test TRSs, malicious attacks can be simulated on diferent scenarios, also in the form of
competition among TRSs [
eBay [44] is a popular and simple, but not robust RS [45, 44, 46], particularly with respect to collusive activities. Its reputation model consists of summing the single feedback provided by counterpart to increase or decrease a reputation score, leaving to each user its evaluation on the basis of their risk attitude. All newcomers receive a null reputation score, i.e. the minimum rating in eBay.
Both PeerTrust [47] and Hypertrust [48] are robust, distributed RS adopting a peer-to-peer overlay network, To identify the most suitable peers to interact, the former exploits several information referred to the specific context, direct feedback, credibility of the indirect feedback sources, number and nature of the transactions performed by each peer. The other one was conceived for large, competitive federations of utility computing infrastructures. In Hypertrust the nodes, linked via overlay, form clusters and a distributed algorithm discovers and allocates resources associated with trusted nodes to limit deceptive activities. The search of potentially interesting resource is reduced to an eligible region based on reputation information.
The well known EigenTrust [16] computes the global reputation of each peer, assuming the reputation transitivity, on the basis of the local trust matrix, storing the (normalized) trust scores that each peer has about the trustworthiness of the other peers in its community, weighted by the trustworthiness of each trustor peer. Based on their reputation scores, the peers will be diferentiated in colluding and not colluding, but its computational process flatten the reputation scores of all the agents including honest ones.
A number of TRSs in distributed, semi-distributed, centralized and/or blockchain-based IoT environment has been presented in [12, 13, 49, 50]. In particular, open IoT environments are particularly risky for the increased possibilities to realize malicious behaviors. In [19], a distributed RS is proposed. It implements some countermeasures to detect malicious or cheating actors. A simulation dealing with vehicular mobility was proposed to test the efectiveness of the reputation model in quickly detecting malicious devices. RESIOT [20] is a framework to form groups of reliable IoT devices based on the reputation scores of their associated agents. In this proposal, a novel reputation model is presented and the results of a set of experiments simulating malicious attacks acting diferent, concomitant cheating strategies, have been compared with those of other RSs. Finally, in [51] a TS for a SIOT scenario is suggested; it adopts a machine learning technique to realize a resilient system towards a significant number of attacks and capable to detect the most part of cheaters at the number of transactions increases.
The TRSs presented in this section implement diferent and efective approaches to identify malicious actors. However, to the best of our knowledge none of them was explicitly designed to preserve the trust scores of honest actors in looking for malicious, unlike the TRS presented in Section 4.
In this section, we describe the agent-based reference scenario which we will refer to in the following. This scenario involves a potentially large number of agents, which can mutually interact among them, on behalf of their associated devices. Within this agent community, we assume that the interactions carried out by agents satisfy the following desirable properties [52]: • agents are long living entities so that past behaviors will provide information about expected, future behaviors; • new agent interactions are driven only by the counterpart’s past behaviors; • agents’ reputation scores are spread into the community.
In particular, we consider rational agents, i.e. artificial intelligence software developed to make autonomous and rational choices on the basis of a system of rules, knowledge and data available. The actions to be taken are chosen on the basis of the information collected, previous knowledge and basic knowledge available to the agent.
The rational agent is composed of interacting elements and is equipped with special devices, such as sensors or actuators, able to (a) capture information from the surrounding environment and (b) intervene to modify it.
In our reference scenario, the information coming from the external environment perceived by the agents can be the reputations of the individual agents belonging to the whole community. As regards the methods of intervention, we refer to the possibility of attributing a high or low trust value based on one’s experience with the individual agent.
With the development of Multi-Agent Systems, several organizational paradigms have been developed. These organizations establish a framework for relationships and interactions between agents. The community we consider is a collection of various agents who interact and communicate. They have diferent goals, they do not have the same level of rationality, nor the same skills, but they are all subject to common laws.
Among the agents of the community there are also the malicious agents (colluding): they gang up and collaborate as their individual interests are shared. Their goal is to maximize the interests of the whole coalition at the expense of other agents.
This section describes in the detail the reputation model we designed to detect colluding agents by preserving the reputation scores of honest agents, wherever other well known approaches decrease them as a collateral efect of their computational processes.
To this end, let an agent community of agents, where each pair of agents is uniquely identified as and , with ̸= ∈ [1, ], and let be a real number ranging in [0; 1] that represents the trust perceived by about , and let = 0 be the trust of an agent about itself for all the agents in .
In the reputation of the generic agent (i.e. the trustee) is computed as the ratio between the sum of the trust values perceived by the other agents of (i.e. the trustors) about , with = 1, . . . , and ̸= , weighted by their own reputation scores, and the sum of the reputation scores of all the trustor agents. More formally, is computed as: , with = 1, . . . , (1) ∑︁ = =1 ∑︁ =1 To represent the agents’ reputation in , we define the trust matrix T = [ ] as: By assuming T as the transpose of the weighted adjacency matrix A = [ ] which, in turn, corresponds to the directed graph , where each node is associated with an agent and each link (, ) is associated with a non-negative value representing the trust value perceived by about , then we can reformulate the equations (1) as:
T = R, ‖R‖1 = 1, (2) where the -th element of the reputation vector R = ( 1, . . . , ) is the reputation of the agent . Note that ‖R‖1 is the sum of the absolute values of the elements of R and its closure to 1 warranties to (2) the uniqueness of the solution. Besides, requiring that the sum of the trust value , given by each agent to the other agents of , be 1, then the matrix T will be column-stochastic. The solution of the eigensystem problem (2) can be reformulated as the computation of the stationary distribution for a Markov chain represented by the matrix T.
For the Perron Frobenius Theorem, = 1 = (T) is an eigenvalue of T (the other eigenvalues will be < 1 in modulus) and if > 0, then a unique vector R ∈ R, ‖R‖1 = 1 there exists, such that T R = (A) R = R, where (A) is the spectral radius that is a unique positive reputation.
A modified version of the eigensystem (2) is the PageRank model that can be formulated as: ︀( T + (1 − ) V U )︀ R = R (3) where the parameter ∈ R ranges in 0 ≤ ≤ 1, U is a unitary vector and V (generally named teleportation vector) is a non-negative vector with unitary 1-norm, i.e. U V = 1. If ̸= 0, 1, the solution (3) exists, and it is unique.
In the PageRank algorithm all the elements of V are set to = 1 . In [53], to decrease the reputation of malicious agents it is proposed to introduce some agents, whose opinions are considered highly reliable. Let ℳ be the set of such mentor agents so that = 1/|ℳ| if the agent belongs to ℳ and 0 otherwise.
To detect colluding agents, the vector R is computed from the matrix T.
To this aim, the agents and are considered as malicious when the following three conditions on the trust scores are verified at the same time: (i) and are high; (ii) and are similar; (iii) the sum of the remaining trust scores from rows and , respectively associated with and , is low.
In other words, we consider all those cases where the trust values of and are high, while the majority of the other agents of consider them untrustworthy.
Therefore, let , , ∈ R ∈ [
The real colluding agents are present among these potential collusive agents and to identify them correctly, we use the third threshold . In order to do this, we first build the vector K = K − Z U. Finally, based on the vector K, we classify as malicious an agent belonging to if ≤ , where is the sum of the remaining trust scores from row associated with , without afecting reputation scores of honest agents.
If we don’t consider the third threshold, we could obtain as malicious colluding agents some honest agents, in particular the good honest agents.
The knowledge of supposed malicious agents can be exploited to provide appropriate reputation vectors.
For instance, let ℬ be the index set of the malicious agents previously identified and let w be the definitive weighted adjacency matrix of the subgraph of consisting of all the both colluded agents and edges connecting them.
We can proceed with two diferent approaches.
For the approach A, consider (3) and a vector L, where its elements are set to 0 if ∈ ℬ or 1/( − |ℬ| ) otherwise. By adopting this setting all the honest agents will receive the same trust score regardless from their starting trust score. This is exactly the same algorithm as EigenTrust, however we exploit here the additional information about the pre-trusted mentors.
The last approach B, consists of building a new matrix T as follows: • Set a threshold > 0; • make the T columns stochastic by normalizing each of them to 1.
• For , ∈ ℬ then let = , otherwise = ; In the following, we present a simple example by considering an agent community formed by twelve agents that is represented in Fig. 1. Moreover, we assume that suspected malicious agents correspond to 30 percent of the total agents and they are identified as 4, 5, 6 and 7.
For simplicity, we choose null the trust that an agent assigns to himself, as it is irrelevant. The corresponding trust matrix is: Determined the threshold and , we can build the following matrix ⎛
0 ⎜ 0.382 ⎜ ⎜ 0.46 ⎜⎜ 0.001 ⎜⎜ 0.002 ⎜ T = ⎜⎜ 0.003 ⎜ 0.002 ⎜ ⎜ 0.01 ⎜ ⎜ 0.02 ⎜ ⎜ 0.03 ⎜ ⎜ 0.04 ⎝ 0.05
Remember that the matrix Z corresponds to a weighted adjacency matrix of the (undirected) subgraph of whose arcs connect potential collusive agents.
With an appropriate choice of , ℬ = {4, 5, 6, 7} is obtained.
Then, applying the approach , set the parameter to 0.2 and considering L = (1/8, 1/8, 1/8, 0, 0, 0, 0, 1/8, 1/8, 1/8, 1/8, 1/8) , the updated trust matrix is computed as:
Finally, by adopting the threshold strategy (approach ) the trust matrix, in correspondence
Note that with approach only the columns of the matrix corresponding to the colluding agents are modified, leaving the columns of the honest agents unchanged. While, with approach , all columns of the matrix are modified and this implies that the final reputation obtained of the agents will be diferent based on the approach used. In Fig. 2 the reputation vectors corresponding to cases A and B are plotted.
Indeed, as concern honest agents, the approach provides very similar reputation, while our approach maintains some diference between the reputations of honest good agents and low honest agents, i.e. it does not penalize the reputation scores of good honest agents.
By interacting with the world around them, agents can form multidimensional, relationship based networks potentially rich of social interactions. In a such agent scenario, the presence of malicious actors should be considered in order to minimize the risks of their deception. Such risks can be increased, for instance in presence of large communities and/or nomadic agents, and their minimization is of primary importance to promote satisfactory social agent interactions. To this purpose, an efective solution is to provide each player with appropriate trust measures about potential its partners and, in this respect, we presented: i) a method to preliminarily identify the best candidates as malicious (colluding) in order to use such agents as pre-trusted mentors; (ii) a novel reputation model to detect colluding malicious agents that does not penalize reputation scores of honest agents in detecting malicious ones.
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