  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 indirect 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. Robust
implementation of direct communication is possible if and only if either the
sender and receiver are directly connected or there exist two disjoint paths
between the sender and the receiver.

Theoretical Economics;Computer Science and Game Theory