Power
Your auction, your rules, right down to the regulation burnt sienna paddles with eggshell lettering. Just kidding, you're not that strict ("Beach-breezy Beige" is also an acceptable color), but the audience does have to play ball when it comes to important guidelines, like "don't touch," "no shoving," and "pay me or else." Your part of the deal is to treat all bidders equally...you can't ignore your nasty neighbor trying to place a bid, or plant a minion in the audience to drive up the prices.
You do have to play nice with the seller, or at least pretend to. Disagreements can arise on both sides, and it takes some skillful compromising to reach a satisfying decision. At the end of your labors, you will have a contract signed by both of you, laying out the rules, so there aren't any nasty surprises, like a seller backing out at the last minute. Hey, if they give you a hard time, you can always buy a stress ball. Maybe in an online auction....