DIY Blog Tour: Reward your hosts
By offering it at this point (when everyone has committed), you lose it as an incentive to get hosts to sign up, but it feels more like a thank you and less like a bribe. People don't like to be bribed, but they love to be thanked. Even the hosts who don't win will appreciate that you recognized their efforts. After all, without them, you wouldn't have a tour.
Even if you can't afford a host contest, make sure you are saying thank you at every opportunity. Being a book blogger can be a thankless job and yet, these individuals give countless hours to the reading community simply because they love it. A thank you is never unwarranted.