Game equilibria for discrete channels

In this paper, the saddle point behavior of mutual information is investigated for discrete channel models. We use the fact that mutual information is a convex function of the channel matrix, and a concave function of the input distribution. Interpreting transmission as a game, nature against the transmitter with payoff given by mutual information, equilibria are shown to exist for certain strategy sets of nature. The case that nature makes the channel useless with zero capacity is discussed in detail. If nature uses a singleton nonzero capacity strategy, a characterization of the capacity-achieving input distribution is derived. Relevant channel classes covered by this approach include the binary asymmetric and erasure channel with bounded error probabilities. Furthermore, for the symmetric n-symbol channel two classes of separation constraints are introduced and the according game equilibria are determined.