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We develop and analyze a trust management protocol for cognitive mission-driven group communication systems (GCSs) in mobile ad hoc networks (MANETs) using hierarchical modeling techniques based on stochastic Petri nets. The goal is to efficiently establish acceptable trust levels among mobile nodes without prior interactions. We seek to identify the optimal length of a trust chain among peers in a trust Web so as to maximize the trust levels for peers on the trust chain, by trading off trust space for trust level. The cognitive nodes in the network can dynamically adapt to changing network environments by adjusting their design parameter settings over time to establish an acceptable trust level with other nodes. We define a trust metric that captures unique characteristics of trust concepts in such MANETs. We demonstrate that an optimal trust chain exists for maximizing the trust metric.