<p>I can't suggest any research papers, but I can suggest one way of studying this problem: using an agent-based model. For example, this is a simple model of an auction on NetLogo: <a href="https://ccl.northwestern.edu/netlogo/models/BiddingMarket" rel="nofollow noreferrer">https://ccl.northwestern.edu/netlogo/models/BiddingMarket</a>. Maybe you can tweak the code to make the model run a simulation of your problem.</p>
<p>If this wasn't what you were looking for, maybe you can try doing a literature search with &quot;agent-based model&quot; in the keyword list. This problem seems like something that can be studied using these models.</p>

CC BY-SA 4.0
2020-09-18T12:50:52.757Z
2020-09-18T12:50:52.757Z
Drashti Shah
<p>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.</p>
<p>Here is a setting that might be of interest: <a href="https://www.jstor.org/stable/1913392" rel="nofollow noreferrer">Kelso &amp; Crawford, Econometrica 1982</a>.
They study <span class="math-container">$m$</span> workers (=buyers in your setting) and <span class="math-container">$n$</span> 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 <a href="https://www.aeaweb.org/articles?id=10.1257/0002828054825466" rel="nofollow noreferrer">&quot;Matching with contracts&quot; by Hatfield &amp; Milgrom, AER 2005</a>.</p>

CC BY-SA 4.0
2020-09-18T09:25:08.747Z
2020-09-18T09:25:08.747Z
Bayesian
<p>This is a reference request.</p>
<p>I'm interested in auction design problems of the following form:</p>
<blockquote>
<p><em>- Consider one seller and many buyers.</em></p>
</blockquote>
<blockquote>
<p><em>- The seller seeks to sell multiple items where each item has multiple units.</em></p>
</blockquote>
<blockquote>
<p><em>- Each buyer is interested in getting <strong>exactly one unit from only one item.</strong></em></p>
</blockquote>
<blockquote>
<p><em>- The seller wants to maximize the social welfare of all buyers.</em></p>
</blockquote>
<p>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.</p>
<p>I'd appreciate any hints of direction where to look. Thank you!</p>

<reference-request><auctions><mechanism-design><matching>
Multi-item multi-unit matching markets
johnny09
# Multi-item multi-unit matching markets

(Asked by: username_0 on 2020-09-18)

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!

**Tags:** reference-request, auctions, mechanism-design, matching

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## 2 answers

### Answer by username_2 on 2020-09-18. Score: 2 | Accepted answer

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 & Crawford, Econometrica 1982](https://www.jstor.org/stable/1913392).
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 ["Matching with contracts" by Hatfield & Milgrom, AER 2005](https://www.aeaweb.org/articles?id=10.1257/0002828054825466).


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### Answer by username_1 on 2020-09-18. Score: 1

I can't suggest any research papers, but I can suggest one way of studying this problem: using an agent-based model. For example, this is a simple model of an auction on NetLogo: <https://ccl.northwestern.edu/netlogo/models/BiddingMarket>. Maybe you can tweak the code to make the model run a simulation of your problem.

If this wasn't what you were looking for, maybe you can try doing a literature search with "agent-based model" in the keyword list. This problem seems like something that can be studied using these models.


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