  Deterministic identification over K-input multiple-access channels with
average input cost constraints is considered. The capacity region for
deterministic identification is determined for an average-error criterion,
where arbitrarily large codes are achievable. For a maximal-error criterion,
upper and lower bounds on the capacity region are derived. The bounds coincide
if all average partial point-to-point channels are injective under the input
constraint, i.e. all inputs at one terminal are mapped to distinct output
distributions, if averaged over the inputs at all other terminals. The
achievability is proved by treating the MAC as an arbitrarily varying channel
with average state constraints. For injective average channels, the capacity
region is a hyperrectangle. The modulo-2 and modulo-3 binary adder MAC are
presented as examples of channels which are injective under suitable input
constraints. The binary multiplier MAC is presented as an example of a
non-injective channel, where the achievable identification rate region still
includes the Shannon capacity region.
