kth price auctions and Catalan numbers

Abdel-Hameed Nawar and Debapriya Sen

MPRA Paper from University Library of Munich, Germany

Abstract: This paper establishes an interesting link between kth price auctions and Catalan numbers by showing that for distributions that have linear density, the bid function at any symmetric, increasing equilibrium of a kth price auction (k is 3 or higher) can be represented as a finite series of k-2 terms whose lth term involves the lth 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 kth price auction for a non-uniform distribution.

Keywords: kth price auction; the revenue equivalence principle; Catalan numbers; Jensen's identity; Hagen-Rothe's identity (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2018-08
New Economics Papers: this item is included in nep-des and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: kth price auctions and Catalan numbers (2018)
Working Paper: $k$th price auctions and Catalan numbers (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:88553

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