(This is a question which overlaps with role-playing games, you will see why when you read it; however this seemed to fit it slightly better.)
My friend mentioned he had a role-playing game which plays like the following: Every player controls one single, shared character. The players take turns to give the character commands on their turn, sometimes rolling dice to decide certain factors e.g. the existence of a certain facility in a town. Each player has a goal which they are attempting to make the character achieve while foiling the other players' goals - however no players are aware of the other players' goals. Each player is also provided with a number of "points" which are used similarly to gambling chips. The person who is prepared to pay the most points takes the next go, but loses the points they played.
My friend is cannot remember the name of the game, but has created a homemade rendition. He is not even sure if it ever existed outside of his mind. My question is, does this game exist, and if so, what is it called?