Communication on networks and strong reliability

We consider sender–receiver games, where the sender and the receiver are two distant nodes in a communication network. We show that if the network has two disjoint paths of communication between the sender and the receiver, then we can replicate all equilibrium outcomes not only of the direct communication game (i.e., when the sender and the receiver communicate directly with each other) but also of the mediated game (i.e., when the sender and the receiver communicate with the help of a mediator).