I see what you are getting at. You could have three egos, two being upset that they are not being used as they think they should.Usually, the stud Closer want to Close, regardless of what team he's on.
Thats good if they are all Stud closers and are willing to settle for lesser roles, it's usually clearly an ego thing.
The Dodgers made it clear in the negotiations with Brian Wilson and Perez that they would not be the closers. They made it clear what their exact role would be. Hopefully they do not get upset as the year goes on.