I play games almost exclusively with my wife and older children. They learn and enjoy playing games like Puerto Rico, Diplomacy, 7 Wonders and Dominion so I am looking for gamer games, not Apples to Apples.
However they don't play most of these games very competitively. Rather, they will often change plans just to be nice to another player.
I have read that some highly recommended gamer games, like Power Grid, really lose a lot if the group isn't playing in highly competetive mode. What are great gamer games that stay great even if the group playing is pretty generous toward each other?
Obviously all great cooperative games would qualify so I am asking about non-cooperative games.
Edit: Certainly having extra players is sometimes a factor (we have 8 children, though only our oldest 3 can play these games with us at this point - of course, that will change in time). However simplified rules is really a non-issue from what we've played so far (Puerto-Rico being the most complex so far). Also we have no qualms about editing a game for family (or for ourselves). e.g. some of the cards in 7 wonders.
Edit. I made part of the question bold just because people kept missing that part and I've noticed those that do are getting downvoted.