$k$th price auctions and Catalan numbers

Abdel-Hameed Nawar and Debapriya Sen

Papers from arXiv.org

Abstract: This paper establishes an interesting link between $k$th price auctions and Catalan numbers by showing that for distributions that have linear density, the bid function at any symmetric, increasing equilibrium of a $k$th price auction with $k\geq 3$ can be represented as a finite series of $k-2$ terms whose $\ell$th term involves the $\ell$th Catalan number. Using an integral representation of Catalan numbers, together with some classical combinatorial identities, we derive the closed form of the unique symmetric, increasing equilibrium of a $k$th price auction for a non-uniform distribution.

Date: 2018-08
New Economics Papers: this item is included in nep-des and nep-gth
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Published in Economics Letters, Volume 172, November 2018, Pages 69-73

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Journal Article: kth price auctions and Catalan numbers (2018)
Working Paper: kth price auctions and Catalan numbers (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1808.05996

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