Off topic but tangentially connected: The group I play with/run for always provides the DM with a list of goals. Each goal falls into at least 1 of the following categories:
[1] Character, Short Term (These goals are ones the character hopes to achieve within the next month or so;
Example- Prevent the King's assassination at next week's tourney, preferably in such a way to earn his favor.)
[2] Character, Long Term (These goals are ones the character shouldn't expect to accomplish for at least a few month if not well beyond his/her lifetime; ;
Example- Gain a high enough position within the king's army to create and control/lead an anti-magic squad.)
[3] Player, Short Term (These goals are ones that a player hopes to achieve within the next few sessions and/or next few levels;
Example- I want to gain patronage from one of the members from the Silver Hand.)
[4] Player, Long Term (These goals are ones that a player aims for over the course of a campaign.
Example- I want to try out my idea for a switch hitter Slayer.)
Now these goals can and will change over the course of playing the game, especially the short term ones. Between the goals we provide the DM and discussing what happened last session from the character's perspective, the DM gains additional insight what is important for his players in that particular game.
OT: There are a lot of inherent problems with running a game with as you described that potentially, as [MENTION=6801611]RedSiegfried[/MENTION] put it, "...it can create some bad feelings between the actual players and lead to an early end to the game. " As I've said before, discussing with your players before the game starts about this idea will alleviate a good many of the risks in such a game. The other way to reduce the risks this game can cause is to work with the individual players to create a secret that they care about at least as much if not more than their character does. If you don't do both, there is a real possibility of unpleasant tension between the player both toward each other and yourself. Some of the problems are as follows:
[1] Forced secret can feel like agency has been stolen from the player (rail roading at a micro scale).
[2] Each player is going to need to separate from the party on multiple occasions to deal with some aspect of their secret (If they don't, the player is less likely to feel invested in the secret... see #4)
[3] More work for you. Unless your players are incredible about not meta gaming, you're going to have to make time either in session or out to deal with what a character does during their secret time.
[4] From my experience, the less invested a player is in a particular aspect of the game (ie their secret) the more likely they will either ignore it or seriously




with it. Neither of these are good, because it means the player isn't having fun... and at worse it might spread to the other players.
[5] There is the risk that a misunderstanding between information your or another players/character provides causes one or more secrets to conflict where you had not intended.
[6] Keeping important secrets over a long period of time causes tension between players/characters. Tension or even outright conflict between characters can often be used to great effect in stories/movies/etc; however, in pen&paper games like these, where each major character is controlled by a person, such tension only detracts from the overall enjoyment of getting together and playing.