  We study nonzero-sum hypothesis testing games that arise in the context of
adversarial classification, in both the Bayesian as well as the Neyman-Pearson
frameworks. We first show that these games admit mixed strategy Nash
equilibria, and then we examine some interesting concentration phenomena of
these equilibria. Our main results are on the exponential rates of convergence
of classification errors at equilibrium, which are analogous to the well-known
Chernoff-Stein lemma and Chernoff information that describe the error exponents
in the classical binary hypothesis testing problem, but with parameters derived
from the adversarial model. The results are validated through numerical
experiments.
