  We introduce a model of interacting random walkers on a finite one
dimensional chain with absorbing boundaries or targets at the ends. Walkers are
of two types: informed particles that move ballistically towards a given
target, and diffusing uninformed particles that are biased towards close
informed particles. This model mimics the dynamics of hierarchical groups of
animals, where an informed individual tries to persuade and lead the movement
of its conspecifics. We characterize the success of the persuasion by the
first-passage probability of the uninformed particle to the target, and we
interpret the speed of the informed particle as a strategic parameter that the
particle tunes to maximize its success. We find that the success probability is
non-monotonic, reaching its maximum at an intermediate speed whose value
increases with the diffusing rate of the uninformed particle. When two
different groups of informed leaders traveling in opposite directions compete,
usually the largest group is the most successful. However, the minority can
reverse this situation and become the most probable winner by following two
different strategies: increasing its attraction strength or adjusting its speed
to an optimal value relative to the majority's speed.
