Specifically the Prisoners Dilemma  are popularly used to link trust with economic utility and demonstrate the rationality behind reciprocity.
For multi-player games, different forms of close market simulations exist . Formal metrics focus on facilitating trust modelling, specifically for large scale models that represent trust as an abstract system e.
Consequently, they may provide weaker insight into the psychology of trust, or in particulars of empirical data collection. Formal metrics tend to have a strong foundations in algebra , probability or logic. There is no widely recognised way to attribute value to the level of trust, with each representation of a 'trust value' claiming certain advantages and disadvantages.
There is also a disagreement about the semantics of some values. The disagreement regarding the attribution of values to levels of trust is specifically visible when it comes to the meaning of zero and to negative values. For example, zero may indicate either the lack of trust but not distrust , or lack of information, or a deep distrust.
Negative values, if allowed, usually indicate distrust, but there is a doubt  whether distrust is simply trust with a negative sign, or a phenomenon of its own. Subjective probability  focuses on trustor's self-assessment about his trust in the trustee. Such an assessment can be framed as an anticipation regarding future behaviour of the trustee, and expressed in terms of probability.
Such a probability is subjective as it is specific to the given trustor, their assessment of the situation, information available to him etc. In the same situation other trustors may have a different level of a subjective probability. Subjective probability creates a valuable link between formalisation and empirical experimentation.
Formally, subjective probability can benefit from available tools of probability and statistics. Empirically, subjective probability can be measured through one-side bets. Assuming that the potential gain is fixed, the amount that a person bets can be used to estimate his subjective probability of a transaction. The logic for uncertain probabilities subjective logic has been introduced by Josang   , where uncertain probabilities are called subjective opinions.
This elegant concept combines probability distribution with uncertainty, so that each opinion about trust can be viewed as a distribution of probability distributions where each distribution is qualified by associated uncertainty. The foundation of the trust representation is that an opinion an evidence or a confidence about trust can be represented as a four-tuple trust, distrust, uncertainty, base rate , where trust, distrust and uncertainty must add up to one, and hence are dependent through additivity.
Subjective logic is an example of computational trust where uncertainty is inherently embedded in the calculation process and is visible at the output. It is not the only one, it is e. Despite the sophistication of the subjective opinion representation, the particular value of a four-tuple related to trust can be easily derived from a series of binary opinions about a particular actor or event, thus providing a strong link between this formal metric and empirically observable behaviour.http://mail.ruk-com.in.th/dios-un-extrao-en-nuestra-casa.php
Finally, there are CertainTrust  and CertainLogic. Hence, there is a bijective mapping between the CertainTrust-triplet and the four-tuple of subjective opinions. Fuzzy systems  , as a trust metrics can link natural language expressions with a meaningful numerical analysis.
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Application of fuzzy logic to trust has been studied in the context of peer to peer networks  to improve peer rating. Also for grid computing  it has been demonstrated that fuzzy logic allows to solve security issues in reliable and efficient manner. The set of properties that should be satisfied by a trust metric vary, depending on the application area.
Following is a list of typical properties. Transitivity is a highly desired property of a trust metric. Without transitivity, trust metrics are unlikely to be used to reason about trust in more complex relationships. The intuition behind transitivity follows everyday experience of 'friends of a friend' FOAF , the foundation of social networks. However, the attempt to attribute exact formal semantics to transitivity reveals problems, related to the notion of a trust scope or context.
For example,  defines conditions for the limited transitivity of trust, distinguishing between direct trust and referral trust. Similarly,  shows that simple trust transitivity does not always hold, based on information on the Advogato model and, consequently, have proposed new trust metrics. It follows everyday intuition and assumes that trust and trustworthiness apply to the whole person, regardless of the particular trust scope or context.
If one can be trusted as a friend, one can be also trusted to recommend or endorse another friend. Therefore, transitivity is semantically valid without any constraints, and is a natural consequence of this approach.
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A contextual approach may, for instance, distinguish between trust in a particular competence, trust in honesty, trust in the ability to formulate a valid opinion, or trust in the ability to provide reliable advice about other sources of information. A contextual approach is often used in trust-based service composition. For a formal trust metric to be useful, it should define a set of operations over values of trust in such way that the result of those operations produce values of trust. Usually at least two elementary operators are considered:. The exact semantics of both operators are specific to the metric.
Even within one representation, there is still a possibility for a variety of semantic interpretations. For example, for the representation as the logic for uncertain probabilities, trust fusion operations can be interpreted by applying different rules Cumulative fusion, averaging fusion, constraint fusion Dempster's rule , Yager's modified Dempster's rule, Inagaki's unified combination rule, Zhang's centre combination rule, Dubois and Prade's disjunctive consensus rule etc.
Each interpretations leads to different results, depending on the assumptions for trust fusion in the particular situatation to be modelled. See   for detailed discussions. The growing size of networks of trust make scalability another desired property, meaning that it is computationally feasible to calculate the metric for large networks.
Scalability usually puts two requirements of the metric:. Attack resistance is an important non-functional property of trust metrics which reflects their ability not to be overly influenced by agents who try to manipulate the trust metric and who participate in bad faith i.
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The free software developer resource Advogato is based on a novel approach to attack-resistant trust metrics of Raph Levien. Levien observed that Google 's PageRank algorithm can be understood to be an attack resistant trust metric rather similar to that behind Advogato. From Wikipedia, the free encyclopedia. Two groups of trust metrics can be identified: Empirical metrics focusing on supporting the capture of values of trust in a reliable and standardized way; Formal metrics that focus on formalization leading to the ease of manipulation, processing and reasoning about trust.
Formal metrics can be further classified depending on their properties. Frontiers vol. University of Stirling PhD thesis. McCroskey, J. Speech Monographs, 33, 65— PGCE 2. MPharm Hons 1. MMath 1.
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