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 nonconvex 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 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.

受网络物理系统安全应用的启发，我们将在干扰器存在的情况下的有限块长度通信问题作为编码器-解码器团队和干扰器之间的零和游戏，通过允许通信团队以及干扰器仅本地随机策略。通信团队的问题在局部随机代码下是非凸的，因此，一般来说，这个游戏不需要极大极小定理。然而，我们证明近似极大极小定理在博弈的极大极小值和极大极值渐近彼此接近的意义上成立。特别是，对于严格低于临界阈值速率，既minimax 和 maximin 值接近于零，对于严格高于零的速率，它们都接近于 1。然后，我们展示了一个二阶极大极小定理，即，对于沿着特定比例精确接近阈值的速率，极大极小值和极大极小值接近相同的常数值，即既不是零也不是一。这些结果的关键是我们对游戏的极大极小值和极大极值的有限块长度边界的推导，以及我们对基于二阶色散的边界的推导。