On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions
证明了在非对称竞拍者、相互依赖估值和关联一维信号的第一价格拍卖中，存在单调出价函数的纯策略均衡，并指出结果无法推广到多维信号或第二价格拍卖。
We establish the existence of pure strategy equilibria in monotone bidding functions in first-price auctions with asymmetric bidders, interdependent values, and affiliated one-dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second-price auctions. Copyright The Econometric Society 2004.