Existence of monotone equilibria in large double auctions
为Reny和Perry（2006）的主要结果提供了一个更短的证明，通过建立拍卖在交易者数量趋于无穷时的下半连续性，并利用了极限拍卖中均衡的存在性，同时去除了原文中的两个假设。
We provide a shorter proof of the main result in Reny and Perry (2006, Econometrica ) by establishing a lower semicontinuity property of auctions as the number of traders goes to infinity, leveraging existence of equilibria in the limit auction. Our proof also eliminates two of the assumptions in their paper.