  Finite blocklength and second-order (dispersion) results are presented for
the arbitrarily-varying channel (AVC), a classical model wherein an adversary
can transmit arbitrary signals into the channel. A novel finite blocklength
achievability bound is presented, roughly analogous to the random coding union
bound for non-adversarial channels. This finite blocklength bound, along with a
known converse bound, is used to derive bounds on the dispersion of discrete
memoryless AVCs without shared randomness, and with cost constraints on the
input and the state. These bounds are tight for many channels of interest,
including the binary symmetric AVC. However, the bounds are not tight if the
deterministic and random code capacities differ.
