In networks without centralized control (e.g. ad-hoc or peer-to-peer networks) the users cannot always be assumed to follow the protocol that they are supposed to. They will cooperate in the operation of the network to the extent that they achieve their own personal objectives. The decision to cooperate depends on the trust relations that users develop for each other through repeated interactions. Users who have not interacted directly with each other can use direct trust relations, generated by others, in a transitive way as a type of recommendation. Network operation and trust generation can be affected by malicious users, who have different objectives, and against whom any proposed solution needs to be robust.

We model the generation of trust relations using repeated games of incomplete information to capture the repetitive operation of the network, as well as the lack of information of each user about the others' objectives. We find equilibria that provide solutions for the legitimate users against which the malicious users cannot improve their gains. The transitive computation of trust is modeled using semiring operators. This algebraic model allows us to generalize various trust computation algorithms. More importantly, we find the maximum distortion that a malicious user can cause to the trust computation by changing the reported trust value of a trust relation.