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No, I am willing to pay $0.01 more but not infinity more, there's a difference

"I made my max bid $500.00, but I'd have paid $500.01!"

"I made my max bid $500.01, but I'd have paid $500.02!"

"I made my max bid $500.02, but I'd have paid $500.03!"

…where does this process end?

The way you've put it, always exactly 1¢ above your max bid.

I can't give you a precise number, but it's somewhere above $0 and below $∞