  Here we consider the task of device-independent certification of the quantum
state distributed in a network when some of the nodes in this network may
collude and act dishonestly. We introduce the paradigm of self-testing with
dishonest parties and present a protocol to self-test the GHZ state in this
framework. We apply this result for state certification in a network with
dishonest parties and also provide robust statements about the fidelity of the
shared state. Finally, we extend our results to the cluster scenario, where
several subgroups of parties may collude during the state certification. Our
findings provide a new operational motivation for the strong definition of
genuine multipartite nonlocality as originally introduced by Svetlichny in [PRD
35, 3066 (1987)].
