Trust Models and Con-Man Agents: From Mathematical to Empirical Analysis

Recent work has demonstrated that several trust and reputation models can be exploited by malicious agents with cyclical behaviour. In each cycle, the malicious agent with cyclical behaviour first regains a high trust value after a number of cooperations and then abuses its gained trust by engaging in a bad transaction. Using a game theoretic formulation, Salehi-Abari and White have proposed the AER model that is resistant to exploitation by cyclical behaviour. Their simulation results imply that FIRE, Regret, and a model due to Yu and Singh, can always be exploited with an appropriate value for the period of cyclical behaviour. Furthermore, their results demonstrate that this is not so for the proposed adaptive scheme. This paper provides a mathematical analysis of the properties of five trust models when faced with cyclical behaviour of malicious agents. Three main results are proven. First, malicious agents can always select a cycle period that allows them to exploit the four models of FIRE, Regret, Probabilistic models, and Yu and Singh indefinitely. Second, malicious agents cannot select a single, finite cycle period that allows them to exploit the AER model forever. Finally, the number of cooperations required to achieve a given trust value increases monotonically with each cycle. In addition to the mathematical analysis, this paper empirically shows how malicious agents can use the theorems proven in this paper to mount efficient attacks on trust models.