## 2 Theoretical Background
### Reputation Systems and Reputation Models  
The main purpose of user reputation systems is to establish trust between unknown parties. Based on a reputation model, a reputation system enables the collection, aggregation, and distribution of data about an entity that can, in turn, be used to identify and predict the future actions of that entity. Using this data, e-commerce users can decide whom they will trust and to what degree. Reputation systems increase or decrease user ratings according to the information collected about the user. They can, therefore, give a positive score, leaving the user with a better ranking, or they can give a negative reputation to punish dishonest behavior. As a result, many online marketplace platforms have developed user reputation management systems that allow trading parties to submit a rating of the counterparty performed in a specific transaction, which is made available to all site visitors. A positive rating of a trading partner is likely to increase trust in the counterparty's performance.  
According to [PERSON] et al. [10], reputation models are composed of three fundamental dimensions: (1) formulation, (2) calculation, and (3) dissemination. In the formulation dimension, the mathematical basis and input types that feed the model are derived. In the calculation dimension, the algorithm of calculation produces a reputation score from the input data. The latter regards the mechanism that allows system participants to obtain the calculated reputation score.  
Regarding the formulation dimension, the authors propose the following types: manual feedback, direct and indirect observations, and inferred data. Reputation systems quantitatively construct sellers' reputations by collecting feedback from buyers with whom the sellers have ever interacted, where feedback is usually presented by a rating that reflects the sellers' performances. The automatic sources are obtained automatically either via direct or indirect observations. In direct observations, automatic sources of information result from data directly observed by an identity, such as the success or failure of an interaction, or the direct observations of cheating. In the case of peer-to-peer (P2P) networks, the measurement of resource utilization is done by neighbors. Information that is obtained second hand or is inferred from first-hand information is classified as indirect. [PERSON] et al. [11] proposed the (3R) model that incorporated observations, based on a buyer's repurchase/product return behavior information, into the calculation dimension in order to mitigate the negative impact of biased ratings.  
[PERSON] et al. [12] proposed two families of reputation systems, explicit and implicit reputation systems. According to the authors, on the one hand, explicit systems have models that follow the same aforementioned principles and dimensions, in which a formulation and calculation have been explicitly defined. On the other hand, the implicit systems are not implemented in network services, but conceptually there is a model of reputation. As examples, the authors give social networks, such as Facebook or LinkedIn, and the Google search engine. In the first case, trust/reputation is inferred through relationships, i.e., friends of friends, while in the search engines, reputation is determined by the number of links that point to the page, and where the links originate. These are examples of automatic observations and inferred data that can enrich the model formulation in the explicit reputation models.  
In the next section, we discuss the formulation and calculation dimensions of the reputation models that are subject to fraud based on several types of attacks and combinations of them.