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$k$th price auctions and Catalan numbers

Abdel-Hameed Nawar and Debapriya Sen

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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.

New Economics Papers: this item is included in nep-des and nep-gth
Date: 2018-08
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http://arxiv.org/pdf/1808.05996 Latest version (application/pdf)

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Journal Article: kth price auctions and Catalan numbers (2018) Downloads
Working Paper: kth price auctions and Catalan numbers (2018) Downloads
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