发表机构
Chinese Academy of Sciences; Institute of Software, Chinese Academy of Sciences; University of Chinese Academy of Sciences（中国科学院; 中国科学院软件研究所; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究精确求解双边贸易中最优固定价格机制的最坏情况福利比率，得到精确值0.7380243357，并通过Wronskian约束与控制问题方法证明，适用于任意有限一阶矩的Borel分布。
AI 中文摘要
先前的研究将双边贸易中最优固定价格机制的最坏情况福利比率置于区间[0.7292,0.73805]内。我们精确确定了该比率，其值为α_FP=0.7380243357…，由显式一维方程的唯根刻画。证明首先饱和了卖方看跌期权与买方看涨期权变换上的Wronskian约束。在逆看涨坐标下，所得极值问题转化为一个控制问题，其对数形式严格凸。其优化器包含一个内部弧段，随后到达边界q=1，轨迹可显式积分。随后，我们通过有界卖方与买方主体以及一个在逃逸值处消失的买方质量来实现该优化器，获得匹配的极限族。每个固定实例均存在最优价格，但最坏情况分布下确界不可达。该证明适用于具有有限一阶矩的任意Borel分布，包括原子分布和无界分布。
英文摘要
Prior work placed the worst-case welfare ratio of the optimal fixed-price mechanism for bilateral trade in the interval [0.7292,0.73805]. We determine the ratio exactly as \[ α_{\mathrm{FP}}=0.7380243357\ldots, \] characterized by the unique root of an explicit one-dimensional equation. The proof first saturates a Wronskian constraint on the seller put and buyer call transforms. In inverse-call coordinates, the resulting extremal problem becomes a control problem whose logarithmic formulation is strictly convex. Its optimizer has one interior arc followed by the boundary \(q=1\), and the trajectory can be integrated explicitly. We then realize this optimizer by a bounded seller and buyer body together with a vanishing buyer mass at an escaping value, obtaining a matching limiting family. Every fixed instance admits an optimal price, but the worst-case distributional infimum is not attained. The proof applies to arbitrary Borel distributions with finite first moment, including atomic and unbounded distributions.
