TR-10-01: A Mathematical Analysis of Computational Trust Models with The Introduction of Con-man Agents

Abstract

Recent work has demonstrated that several trust and reputation models can be exploited by malicious agents with cyclical behaviour if the details of the trust model are known to the malicious agents. In each cycle, a malicious agent with cyclical behaviour first regains a high trust value with a number of cooperations and then misuses its gained trust by engaging in a bad transaction. Using a game theoretic formulation, Salehi-Abari and White have proposed an adaptive trust and reputation model, called AER, 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 the cyclical behaviour. Furthermore, their results demonstrate that this is not so for AER. This paper provides a mathematical analysis of the properties of the Yu and Singh scheme, Regret, FIRE, probabilistic trust models, and the AER scheme when faced with cyclical behaviour by malicious agents. Three main results are proven. First, malicious agents can always select a cycle period that allows them to exploit the Yu and Singh model, Regret, FIRE, and probabilistic trust models indefinitely. Second, malicious agents cannot select a single, finite cycle period that allows them to exploit AER forever; their exploitation time is bounded. Finally, the number of cooperations required to achieve a given trust value increases monotonically with each cycle in AER.

TR-10-01.pdf