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

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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 k2 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 nonuniform distribution.
Item Type:  MPRA Paper 

Original Title:  kth price auctions and Catalan numbers 
Language:  English 
Keywords:  kth price auction; the revenue equivalence principle; Catalan numbers; Jensen's identity; HagenRothe's identity 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  88553 
Depositing User:  Debapriya Sen 
Date Deposited:  29 Aug 2018 06:23 
Last Modified:  28 Sep 2019 03:02 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/88553 