发表机构
Beijing Institute of Technology; Renmin University of China（北京理工大学; 中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究确定了双边与匹配市场中次优与最优福利的尖锐比率，在任意先验下约为0.888，在单调风险率下约为0.911，并提供了证明与数值验证方法。
AI 中文摘要
当价值为私有时，市场必须损失多少社会福利？我们在独立非负类型、贝叶斯激励相容、中期个体理性以及无预期预算赤字条件下，确定了次优福利与最优福利的尖锐比率。对于任意先验分布，该比率约为 $0.8882516903$；当买家具有单调风险率且卖家不受限制时，该比率约为 $0.9113893681$。任意先验保证适用于每个向下封闭的可行匹配族；单调风险率保证在兼容图的每个匹配均可行时成立。这两个常数在双边贸易中已经达到尖锐。证明将卖家的初始禀赋保留在预算拉格朗日函数中。对于任意先验，一个共同的阈值分解将问题简化为三参数幂律分布。对于单调风险率，买家和卖家得分的共同变换将其简化为移位封顶指数买家；一个类型级分配证书和一个显式的最坏情况卖家满足相同的边界方程。双边到匹配的框架，带有福利禀赋费用和保持单调风险率的打包论证，无损失地转移了这些仿射不等式。我们给出了这两个常数的精确变分特征，以及用于数值评估的可复现区间证书。不受限制的有符号转移也允许逐点强预算平衡。
英文摘要
How much social welfare must a market lose because values are private? We determine the sharp ratio of second-best to first-best welfare under independent nonnegative types, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. The ratio is approximately $0.8882516903$ for arbitrary priors and $0.9113893681$ when buyers have monotone hazard rates and sellers are unrestricted. The arbitrary-prior guarantee holds for every downward-closed family of feasible matchings; the MHR guarantee holds when every matching of a compatibility graph is feasible. Both constants are \revise{attained}{sharp} already in bilateral trade. The proof keeps the sellers' initial endowment inside the budget Lagrangian. For arbitrary priors, a common threshold decomposition reduces the problem to three-parameter power-law distributions. For monotone hazards, common transformations of buyer and seller scores reduce it to shifted capped exponential buyers; a typewise allocation certificate and an explicit worst-case seller satisfy the same boundary equation. The bilateral-to-matching framework, with a welfare endowment charge and an MHR-preserving packing argument, transfers these affine inequalities without loss. We give exact variational characterizations of both constants and reproducible interval certificates for their numerical evaluation. Unrestricted signed transfers also permit pointwise strong budget balance.
