Room 25

From BoardGameGeek:

Trapped in a prison in which each room has four doors but apparently no exit, the players must try to find Room 25, the supposed exit to this nightmare. But some amongst them might be guardians of the prison, waiting for the right moment to strike. In the cooperative game Room 25, not everyone wants to escape from imprisonment – but who is the traitor? Each turn, the player moves are preprogrammed, requiring discussion, negotiation – and possibly betrayal. Room 25 includes five different playing modes, from full cooperation to a solitaire game.