  We investigate a modified spatial stochastic Lotka-Volterra formulation of
the rock-paper-scissors model using off-lattice stochastic simulations. In this
model one of the species moves preferentially in a specific direction -- the
level of preference being controlled by a noise strength parameter $\eta \in
[0, 1]$ ($\eta = 0$ and $\eta = 1$ corresponding to total preference and no
preference, respectively) -- while the other two species have no referred
direction of motion. We study the behaviour of the system starting from random
initial conditions, showing that the species with asymmetric mobility has
always an advantage over its predator. We also determine the optimal value of
the noise strength parameter which gives the maximum advantage to that species.
Finally, we find that the critical number of individuals, below which the
probability of extinction becomes significant, decreases as the noise level
increases, thus showing that the addition of a preferred mobility direction
studied in the present paper does not favour coexistence.
