Multi-item multi-unit matching markets This is a reference request.
I'm interested in auction design problems of the following form:

- Consider one seller and many buyers.


- The seller seeks to sell multiple items where each item has multiple units.


- Each buyer is interested in getting exactly one unit from only one item.


- The seller wants to maximize the social welfare of all buyers.

Has this problem been studied in the literature? I have tried looking at combinatorial auctions, matching markets, and multi-parameter markets but so far haven't been lucky.
I'd appreciate any hints of direction where to look. Thank you!
I gave you an extremely vague lead in my other comment. Thinking about it a bit harder, I beieve you are right with having a look into the matching literature which I know a bit less.
Here is a setting that might be of interest: Kelso &amp; Crawford, Econometrica 1982.
They study $m$ workers (=buyers in your setting) and $n$ firms (=items), where a worker can only work at one firm, but a firm can hire many workers. Firms pay salaries to workers (=accept payments for a unit). If that is a setting that appeals to you, go straight to &quot;Matching with contracts&quot; by Hatfield &amp; Milgrom, AER 2005.