Nash Codes for Noisy Channels

This paper studies the stability of communication protocols that deal with transmission errors. We consider a coordination game between an informed sender and an uninformed receiver, who communicate over a noisy channel. The sender’s strategy, called a code, maps states of nature to signals. The receiver’s best response is to decode the received channel output as the state with highest expected receiver payoff. Given this decoding, an equilibrium or “Nash code” results if the sender encodes every state as prescribed. We show two theorems that give sufficient conditions for Nash codes. First, a receiver-optimal code defines a Nash code. A second, more surprising observation holds for communication over a binary channel, which is used independently a number of times, a basic model of information transmission: under a minimal “monotonicity” requirement for breaking ties when decoding, which holds generically, every code is a Nash code.