When my kids have had birthday parties and such, I've had prizes for the highest scores but I didn't do it in an organized tournament format. If your whole purpose is to have a tournament, then what you are saying makes some sense along with needing to come up with a competition format. If you are having a general party and want to encourage the kids to play the pinball machines here is what we do:

We explain to the kids that there will be a prize(s) for high scores at least one of my games. This would include usually about 5 pinball machines and 5 video arcades. Some kids are interested in playing these for long periods of time, while others are just as interested in ping pong, pool, foosball, and xbox360 in the basement. Free choice is fine, however in my house only guests playing the pins/vids can be rewarded with a prize. In my game room I have a chalkboard with the name of each pin/vid written and a space for player name and high score. As players knock one another off the board, they update it with name and score. At the end of the night, I'll draw out the name of a random game or 2 from a hat and whoever has the high score on that particular machine wins a gift card or other prize.

This format does a few things. It keeps people from hogging a particular machine all night. It encourages everyone to try as many games as possible. And it often results in some random person that just happened to do well on something they may have gotten lucky on.