  As the behavior of a system composed of cyclically competing species is
strongly influenced by the presence of fluctuations, it is of interest to study
cyclic dominance in low dimensions where these effects are the most prominent.
We here discuss rock-paper-scissors games on a one-dimensional lattice where
the interaction rates and the mobility can be species dependent. Allowing only
single site occupation, we realize mobility by exchanging individuals of
different species. When the interaction and swapping rates are symmetric, a
strongly enhanced swapping rate yields an increased mixing of the species,
leading to a mean-field like coexistence even in one-dimensional systems. This
coexistence is transient when the rates are asymmetric, and eventually only one
species will survive. Interestingly, in our spatial games the dominating
species can differ from the species that would dominate in the corresponding
nonspatial model. We identify different regimes in the parameter space and
construct the corresponding dynamical phase diagram.
