Revenue-maximizing auction with no free disposal

Myerson has a famous theory that can be used to design truthful auctions maximizing the revenue of the seller. The simplest case is when a seller sells a single item to buyers whose values are independent identically-distributed random variables. In this case, Myerson's auction is equivalent to a second-price auction with a reserve price, where the reserve price is determined by the distribution (for example, if all buyers' valuations are distributed uniformly between 0 and 100, then the revenue-maximizing auction is a second price auction with reserve price 50).

Implementing this optimal auction may require to destroy the item, in case all buyers bid below the reserve price. But discarding items might be impossible or illegal. For example, according to John Locke, the "natural law" allows a person to appropriate parts of nature for his personal use, but does not allow to destroy items.

This raises the following question: what is a revenue-maximizing auction in a situation in which it is not allowed to discard items?

• Are you familiar with the revenue equivalence theorem? If yes: what are the exact conditions that stop us from doing a first or second-price auction without a reserve price? Commented Feb 25, 2022 at 12:18
• @Giskard sure, we can do a second-price auction without a reserve price, but the expected revenue will be lower than with the optimal reserve price. My question is: what is the truthful auction that maximizes the revenue, under the constraint that the item must be sold? Is it indeed the second-price auction without reserve prices? Commented Feb 25, 2022 at 12:58
• @Giskard: Under standard IPV assumptions, the (first- or) second-price auction without a reserve price is not revenue-maximizing. Being familiar with the RET doesn't help here. Commented Feb 25, 2022 at 13:35
• @ErelSegal-Halevi: Why should it sometimes be necessary to destroy the item? As I understand the model, the item is sometimes just not sold (and the seller keeps it). Commented Feb 25, 2022 at 13:38
• @Giskard the RET says that, if the allocations of two auctions are identical, then their revenues are identical too. But with reserve prices, the allocations are not identical to an auction without reserve prices. Commented Feb 26, 2022 at 21:03