kth price auctions and Catalan numbers

Nawar, Abdel-Hameed and Sen, Debapriya (2018): kth price auctions and Catalan numbers. Forthcoming in: Economics Letters

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: kth price auction; the revenue equivalence principle; Catalan numbers; Jensen's identity; Hagen-Rothe's identity
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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