Equilibrium Existence in First‐Price Auctions With Private Values
研究了私人价值第一价格拍卖中均衡存在的充分条件，允许非拟线性效用和含原子、正负相关的价值分布，并发现均衡存在性常取决于高价值分布支撑中的最小值。
We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.