To encourage houseguests to compete, have a points system where a houseguest gains points for every competition won.
5 points for HOH, 5 points for POV, 3 points for have/have not, 2 points for coming in second in HOH or POV.
Where points would apply is if the houseguests are in a competition and it comes down to a tie-breaker question.
Instead of answering a question where the answer is a number, the houseguest with the most points could choose a tie-breaker game.
It could be something that houseguest is good at, like throwing darts (I don't think they have a dartboard in the BB house).
Or free throws at a basketball net (they had a basketball net in BB2, they could bring it back).
Or a quick hand of blackjack where the houseguest with the most points gets to be dealer and in blackjack, tie goes to the dealer.
Or a quick game of 3 ball on the pooltable where the person with the most points gets to break.
Or a trivia question where the person with the most points gets to pick the category.
Or some other game I haven't thought of.