One thing I wouldn’t do is let the problem slide, because it would only get worse and overlooking it would set a bad precedent. I would try again and again and again, in whatever way I could, to solve the problem, involving wider and wider circles of people, both above and below the offending executive and including my own boss if necessary, so that everyone involved can see the rewards for teamwork and the drawbacks of non-cooperation.
I might add that I’ve never yet come across a situation that couldn’t be resolved by harnessing others in a determined, constructive effort.