  We study the capacity region $C_L$ of an arbitrarily varying multiple-access
channel (AVMAC) for deterministic codes with decoding into a list of a fixed
size $L$ and for the average error probability criterion. Motivated by known
results in the study of fixed size list decoding for a point-to-point
arbitrarily varying channel, we define for every AVMAC whose capacity region
for random codes has a nonempty interior, a nonnegative integer $\Omega$ called
its symmetrizability. It is shown that for every $L \leq \Omega$, $C_L$ has an
empty interior, and for every $L \geq (\Omega+1)^2$, $C_L$ equals the
nondegenerate capacity region of the AVMAC for random codes with a known
single-letter characterization. For a binary AVMAC with a nondegenerate random
code capacity region, it is shown that the symmetrizability is always finite.
