  Motivated by applications in the security of cyber-physical systems, we pose
the finite blocklength communication problem in the presence of a jammer as a
zero-sum game between the encoder-decoder team and the jammer, by allowing the
communicating team as well as the jammer only locally randomized strategies.
The communicating team's problem is non-convex under locally randomized codes,
and hence, in general, a minimax theorem need not hold for this game. However,
we show that approximate minimax theorems hold in the sense that the minimax
and maximin values of the game approach each other asymptotically. In
particular, for rates strictly below a critical threshold, both the minimax and
maximin values approach zero, and for rates strictly above it, they both
approach unity. We then show a second order minimax theorem, i.e., for rates
exactly approaching the threshold with along a specific scaling, the minimax
and maximin values approach the same constant value, that is neither zero nor
one. Critical to these results is our derivation of finite blocklength bounds
on the minimax and maximin values of the game and our derivation of second
order dispersion-based bounds.
