Zero Error Strategic Communication

Abstract

We introduce a new setting in information theory where a receiver tries to exactly recover a source signal from a dishonest sender who sends messages with an intention to maximize its utility. The sender can send messages to the receiver over a noiseless channel whose input space is the entire signal space, but due to its dishonesty, not all signals can be recovered. We formulate the problem as a game between the sender and the receiver, where the receiver chooses a strategy such that it can recover the maximum number of source signals. We show that, despite the strategic nature of the sender, the receiver can recover an exponentially large number of signals. We show that this maximum rate of strategic communication is lower bounded by the independence number of a suitably defined graph on the alphabet and upper bounded by the Shannon capacity of this graph. This allows us to exactly characterize the rate of strategic communication for perfect graphs.