Communicating with a Strategic Sender

Abstract

We consider a communication problem over a noiseless rate limited channel where the sender and receiver have misaligned objectives - the receiver wants to compute a function of the source, but the sender acts to maximize its own utility function. This setting is distinct from source coding since the sender and receiver are strategic agents and hence Shannon theory does not apply. We show that despite this, under certain conditions, reliable communication can be ensured. We pose the problem as a leader-follower game between the sender and receiver. We show that when the receiver is the leader, and the function is incentive compatible, every equilibrium of this game is an optimal code for the source-coding problem. This shows that the Shannon rate is a fundamental threshold for this communication. We show that the incentive compatibility condition, which has its origin in mechanism design theory, is also necessary for reliability. We also show that to ensure reliable communication, it is essential that the receiver is the leader, since the same may not be ensured when the sender is the leader.