  We consider a class of multi-particle reinforced interacting random walks. In
this model, there are some (finite or infinite) particles performing random
walks on a given (finite or infinite) connected graph, so that each particle
has higher probability to visit neighboring vertices or edges which have been
seldom visited by the other particles. Specifically we investigate two
particles' vertex-reinforced interacting random walks on finite complete
graphs. By a dynamical approach we prove that the two particles' occupation
measure asymptotically has small joint support almost surely if the
reinforcement is strong.
