We consider sender-receiver games, where the sender and the receiver are two distinct nodes in a communication network. Communication between the sender and the receiver is thus indirect. We ask when it is possible to robustly implement the equilibrium outcomes of the direct communication game as equilibrium outcomes of in- direct communication games on the network. Robust implementation requires that: (i) the implementation is independent of the preferences of the intermediaries and (ii) the implementation is guaranteed at all histories consistent with unilateral deviations by the intermediaries. We show that robust implementation of direct communication is possible if and only if either the sender and receiver are directly connected or there exist two dis- joint paths between the sender and the receiver. We also show that having two disjoint paths between the sender and the receiver guarantees the robust implementation of all communication equilibria of the direct game. We use our results to reflect on organizational arrangements.
(joint with Ludovic Renou and Xavier Venel)