Big Brother is a reality TV show. I like to think of them as today's game shows, myself. They have play at home games for those, so why not play at home survivor or Big Brother?
There are a couple problems with the setup, though. After all, once you are evicted, that's the end of the game for you. Also, keeping people locked in your house for 13 weeks is generally frowned upon. So there would be some timing issues to work out, maybe every half-hour or hour instead of a week.
The main points of the game are these:
Every week there is a competition to decide who is the Head of Household. The Head of Household is safe from eviction for the week, but must nominate two other players for eviction.
After the nominations, there is a competition for the Power of Veto. The Head of Household and the two nominees play, with each picking a partner(either at random or their choice - depends which season you watch.) However, the competition is a free for all. Whoever wins the power of veto can veto one of the nominations. If you use the Power of Veto, you cannot be nominated. The Head of Household then nominates someone else to fill the void. The player does not HAVE to use the PoV.
After the veto ceremony, the other players (not nominated and not Head of Household) vote for who they want to evict. Head of Household breaks ties.
Then, the cycle starts over with one less player in the house, and the current HoH cannot compete for the next week's HoH.
When there are 3 players left, a special competition decides who is Head of Household, because it's so important. Whoever is Head of Household gets to eliminate whoever they want.
When there are 2 players left, the last 7 evicted players vote for a winner.
In the show they are always throwing in twists and turns, because it's a show, but the at home version wouldn't need much more than this. The show is incredibly fun to watch, to me. It's fun to think about how cool it would be to play, and how much better I would be than everyone on it (even though I probably wouldn't be).
The hangup I have is that I can't think of enough cool competitions for everyone to do. I was trying to think of indoor board-gamey type things, card games... The show involves a lot of physically challenging events, but mixes in mental ones too. I think the people more interested in this game would be the type of people who don't like physical challenges... most of the game is mental. Who do I put up? Do I use the veto? Should I ally myself with someone?
Oh well. It would be fun, but until I get there, I'll stick with Diplomacy. Same concept (who should I ally with? Who should I attack? Do I save this person from that person?), different mechanism.