Two auctions with the same interim allocation probabilities and the same lowest-type utilities have the same interim expected payments under the usual risk-neutral single-parameter incentive conditions. Equal realized payments are not required. This conclusion follows directly from the interim payment identity.
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Revenue equivalence is a fundamental concept in auction theory and game theory that states that under certain conditions, different types of auction formats will yield the same expected revenue for the seller. The idea is based on several assumptions about the bidders' behavior and the auction environment.