I run ours just like a traditional auction, but students purchase items using raffle tickets instead of money. Students earn five tickets every Monday morning for returning a signed weekly report from their Friday Folder. They can earn additional tickets for showing life skills (cooperation, responsibility, perseverance, etc.). Students can also lose tickets in our room, but that doesn't happen very often. At the end of each nine weeks, it's time to bid on prizes.
The prizes don't have to be anything expensive. I auction classroom freebies like homework passes, sitting in the teacher chair for a day, extra recesses, writing in ink for a day, and anything else each particular group of students seems to like. I also ask parents to contribute items from home such as gently used toys, books the family has outgrown, or dollar store items. I also stockpile items for the auction throughout the year. I'm always getting free stickers, posters, magazines, canvas totes, and other "teacher" stuff the students want. Shells from the beach have also been a big hit in our room.
If you're looking for a way to shake up your behavior management routine, you might want to consider classroom auctions. The students always count down to the next one because they're so much fun!