<p>In addition to @Tomcat's suggestions, you may also want to check out the literature on matching markets.</p>
<p>Easley and Kleinberg have an <a href="https://www.cs.cornell.edu/home/kleinber/networks-book/" rel="nofollow noreferrer">introductory textbook</a>* on the subject. Chapter 10 covers the basic model of matching markets. Chapter 15 goes over the auction of ad slots as an application.</p>
<hr />
<p>*Easley, David, and Jon Kleinberg (2010) <a href="https://www.cs.cornell.edu/home/kleinber/networks-book/" rel="nofollow noreferrer"><em>Networks, Crowds, and Markets: Reasoning About a Highly Connected World</em></a>, Cambridge University Press.</p>

CC BY-SA 4.0
2020-08-11T06:55:40.637Z
2020-08-11T06:55:40.637Z
Herr K.
<p>I suggest to have a look at <a href="https://www.elsevier.com/books/auction-theory/krishna/978-0-12-374507-1" rel="nofollow noreferrer">Krishna's &quot;Auction Theory&quot;</a>, Chapter 16 &quot;Non-identical items&quot;. Regarding your particular multiproduct problem, I would go from <a href="https://www.jstor.org/stable/2171924" rel="nofollow noreferrer">Armstrong's &quot;Multiproduct nonlinear pricing&quot;, Econometrica 1996,</a> and see what happens.</p>
<p>While I don't want to discourage you, let me mention that mechanism design with multidimensional types is very, very difficult and can get quite &quot;ugly&quot;. See my reply <a href="https://economics.stackexchange.com/a/39643/11590">here</a>. It may not be the kind of problem you want to tackle after you have &quot;only started reading it a few days ago&quot;. However, it is quite an important problem and more good research is needed. So I am rooting for you!</p>

CC BY-SA 4.0
2020-09-17T22:25:52.220Z
Thanks for your answer. Hoping you don't mind but are you aware of any paper studying multi-item, multi-unit auctions in which bidders are only interested in one unit from only one item?
johnny09
CC BY-SA 4.0
2020-09-18T09:01:35.737Z
Off the top of my head I don't think I know such a paper. I would start searching on google.scholar, looking at papers that cite (or are cited) by Thanassoulis, JET 2004, and Carroll, Ecta 2017. Certainly a difficult setting for a mechanism-design setting.
Bayesian
CC BY-SA 4.0
2020-09-10T09:17:43.380Z
2020-09-10T09:17:43.380Z
Bayesian
<p>For single unit demand see Maskin and Riley's &quot;Optimal multi-unit Auctions&quot;.</p>

CC BY-SA 4.0
2021-07-26T00:03:09.090Z
2021-07-26T00:03:09.090Z
user36522
<p>I'm new to auction theory and only started reading it a few days ago.</p>
<p><strong>My question is this:</strong> <em>Is it possible to design efficient auctions of multiple non-identical items? By efficient I mean maximize the social welfare.</em></p>
<p>Also, let's say there is only one seller who owns all items and seeks to sell them to multiple bidders who can get at most one item.</p>
<p>I'm a little discouraged as I haven't found a lot of theory papers on this problem. Is it because what I described above is a special of bundling (where bundle sets are singletons)?</p>
<p>I'd appreciate it immensely if you could direct me to a source (paper or book). Thank you.</p>

<auctions><mechanism-design>
Multi-item Auctions in Mechanism Design
johnny09
# Multi-item Auctions in Mechanism Design

(Asked by: username_0 on 2020-08-10)

I'm new to auction theory and only started reading it a few days ago.

**My question is this:** *Is it possible to design efficient auctions of multiple non-identical items? By efficient I mean maximize the social welfare.*

Also, let's say there is only one seller who owns all items and seeks to sell them to multiple bidders who can get at most one item.

I'm a little discouraged as I haven't found a lot of theory papers on this problem. Is it because what I described above is a special of bundling (where bundle sets are singletons)?

I'd appreciate it immensely if you could direct me to a source (paper or book). Thank you.

**Tags:** auctions, mechanism-design

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## 3 answers

### Answer by username_1 on 2020-08-11. Score: 4

In addition to @Tomcat's suggestions, you may also want to check out the literature on matching markets.

Easley and Kleinberg have an [introductory textbook](https://www.cs.cornell.edu/home/kleinber/networks-book/)\* on the subject. Chapter 10 covers the basic model of matching markets. Chapter 15 goes over the auction of ad slots as an application.

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\*Easley, David, and Jon Kleinberg (2010) [*Networks, Crowds, and Markets: Reasoning About a Highly Connected World*](https://www.cs.cornell.edu/home/kleinber/networks-book/), Cambridge University Press.


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### Answer by username_2 on 2020-09-10. Score: 3

I suggest to have a look at [Krishna's "Auction Theory"](https://www.elsevier.com/books/auction-theory/krishna/978-0-12-374507-1), Chapter 16 "Non-identical items". Regarding your particular multiproduct problem, I would go from [Armstrong's "Multiproduct nonlinear pricing", Econometrica 1996,](https://www.jstor.org/stable/2171924) and see what happens.

While I don't want to discourage you, let me mention that mechanism design with multidimensional types is very, very difficult and can get quite "ugly". See my reply [here](https://economics.stackexchange.com/a/39643/11590). It may not be the kind of problem you want to tackle after you have "only started reading it a few days ago". However, it is quite an important problem and more good research is needed. So I am rooting for you!

> **Comments:**
> **username_0**: Thanks for your answer. Hoping you don't mind but are you aware of any paper studying multi-item, multi-unit auctions in which bidders are only interested in one unit from only one item?  
> **username_2**: Off the top of my head I don't think I know such a paper. I would start searching on google.scholar, looking at papers that cite (or are cited) by Thanassoulis, JET 2004, and Carroll, Ecta 2017. Certainly a difficult setting for a mechanism-design setting.  

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### Answer by username_3 on 2021-07-26. Score: 0

For single unit demand see Maskin and Riley's "Optimal multi-unit Auctions".


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