摘要翻译：
本文在$k$th价格拍卖和加泰罗尼亚数之间建立了一种有趣的联系，证明了对于具有线性密度的分布，$k\geq3$$th价格拍卖在任意对称的递增均衡下的出价函数可以表示为一个$k-2$项的有限级数，其$ell$th项涉及$ell$th加泰罗尼亚数。利用Catalan数的积分表示，结合一些经典的组合恒等式，给出了非均匀分布的k$th价格拍卖的唯一对称递增平衡点的封闭形式。
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英文标题：
《$k$th price auctions and Catalan numbers》
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作者：
Abdel-Hameed Nawar, Debapriya Sen
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最新提交年份：
2018
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分类信息：

一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/1808.05996