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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.

johnny09
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4 Answers4

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There’s a large literature on this in both CS and Economics. For economics, a good starting point would be Vijay krishna’s Auction Theory book (2009 edition). It has a whole section on multi-object auctions.

For CS, check out some of the papers by Jason Hartline. He may have lecture notes as well. Naom Nisan and others have a book called algorithmic game theory where some chapters (if I remember correctly) deal with multi-object auctions.

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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* on the subject. Chapter 10 covers the basic model of matching markets. Chapter 15 goes over the auction of ad slots as an application.

*Easley, David, and Jon Kleinberg (2010) Networks, Crowds, and Markets: Reasoning About a Highly Connected World, Cambridge University Press.

Herr K.
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I suggest to have a look at Krishna's "Auction Theory", Chapter 16 "Non-identical items". Regarding your particular multiproduct problem, I would go from Armstrong's "Multiproduct nonlinear pricing", Econometrica 1996, 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. 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!

Bayesian
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  • 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 Sep 17 '20 at 22:25
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    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 Sep 18 '20 at 09:01
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For single unit demand see Maskin and Riley's "Optimal multi-unit Auctions".

user36522
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