  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 decision maker, the 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.
