Our paper belongs to the strand of literature associated with the notion of Nash networks introduced by Bala and Goyal [1] in the connections model. Our aim is to consider situations where agent i has concerns about the validity of information that she acquires from agent j. Independently conrming this information through another set of agents allows i to put more faith in j's information, that is increases the value of j's information. In such situations, we characterize the set of strict Nash networks. Then, we provide a condition which ensures the existence of Nash networks when agents play pure strategies. Finally, we characterize the set of strict ecient networks and we discuss the relationship between ecient networks and strict Nash networks.
