In descending order of quality, the ideas I have so far are:

Idea #1: The player’s goal is to keep several people alone, and to prevent them from contacting each other. The game would take place on a maze on a grid (although, if possible, the graphics would be smooth). New people would be introduced as the game goes on, and the player would be charged with keeping them separate for as long as possible. It would likely be a turn-based type of game where there are two stages. In one, the player places obstacles and stuff, in the other, the entities move. There would be penalties for killing people.

Idea #2: Something about splinter cells or something; trying to function without knowing anything about other members of same “team”.

Idea #3: A damsel in distress self-rescues.