This is an experiment, involving you the GM and your players. The first step is to go to Storytelling Games
where you'll find links to storytelling games of all sorts, some free. The free ones it shouldn't take you long to get the rules which you can then learn and prepare to teach your players.
The second step is to invite your players to a special session of your campaign. In this session a friend of the players' characters has invited those characters to his house to play this storytelling game he recent got ahold of. The players go there as there characters where they are introduced to this storytelling game and taught how to play. Once they now the game (really shouldn't be hard) they then, as their characters, play the game by telling a story according to the game's rules.
Now as all this is going on carefully observe what your players are doing. How are they behaving, acting as their characters when they are just being their characters, and how do they behave when they are being their characters telling a story.
Do I have a reason for this?
Yes, I do. But I'm going to let you discover it for yourself, by having you run this experiment for yourself instead of accepting my word for it.
You are right, I am evil, and I like it!
Give it a try, see what happen, and report on your observations. Ask your players what they think and report their observations. I expect that what you learn could surprise you.