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We study the capacity region <formula formulatype="inline"><tex Notation="TeX">$C_{L}$</tex></formula> of an arbitrarily varying multiple-access channel (AVMAC) for deterministic codes with decoding into a list of a fixed size <formula formulatype="inline"><tex Notation="TeX">$L$</tex></formula> 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 <formula formulatype="inline"><tex Notation="TeX">$\Omega$</tex></formula> called its symmetrizability. It is shown that for every <formula formulatype="inline"><tex Notation="TeX">$L\leq\Omega$</tex></formula>, <formula formulatype="inline"><tex Notation="TeX">$C_{L}$</tex> </formula> has an empty interior, and for every <formula formulatype="inline"><tex Notation="TeX">$L\geq(\Omega+1)^{2}$</tex></formula>, <formula formulatype="inline"><tex Notation="TeX">$C_{L}$</tex> </formula> 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.

On the Deterministic Code Capacity Region of an Arbitrarily Varying Multiple-Access Channel Under List Decoding