  Two infinite walks on the same finite graph are called compatible if it is
possible to introduce delays into them in such a way that they never collide.
Years ago, Peter Winkler asked the question: for which graphs are two
independent walks compatible with positive probability. Up to now, no such
graphs were found. We show in this paper that large complete graphs have this
property. The question is equivalent to a certain dependent percolation with a
power-law behavior: the probability that the origin is blocked at distance n
but not closer decreases only polynomially fast and not, as usual,
exponentially.
