The discrete additive multiple-access arbitrarily varying channel (AVC) with two senders and one receiver is considered. Necessary and sufficient conditions are given for its deterministic-code average-probability-of-error capacity region under a state constraint to have a nonempty interior. In the case that no state constraint is present, the capacity region is characterized exactly. In the case of the noiseless mod-2 adder AVC using state constraint function l(s)=s and subject to a state constraint L less than or equal to 0.13616917, the capacity region is shown to be a 45-degree triangle whose legs have length 1-h(L), where h denotes the binary entropy function.
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