Robust communication on networks

TL;DR

This paper investigates conditions under which direct communication outcomes can be robustly implemented in indirect network settings, emphasizing network connectivity and path disjointness for reliable communication.

Contribution

It characterizes the exact network conditions, such as direct links or disjoint paths, necessary for robust implementation of direct communication outcomes.

Findings

Robust implementation is possible if sender and receiver are directly connected.

Disjoint paths between sender and receiver enable robust indirect communication.

The paper provides necessary and sufficient network conditions for implementation.

Abstract

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.