Collaborative play can mean many things. If we're running an evil campaign, then it may be that both the wizard and the fighter are looking for ways to screw the other over, because that is the expectation.
In a non-evil campaign, it might mean that we're all creating a shared narrative surrounding the characters, but nothing more. The wizard player doesn't have any obligation towards making sure that the fighter player has a good time, unless that's part of that table's contract.
Ideally the players are collaborating towards a satisfying experience, but I've known plenty of players over the years who prioritize their own satisfaction. This is purely anecdotal, but I've noticed that those players tend to favor wizards (and to a lesser extent, rogues).