分散信息下互补分配中的近似最优福利
Approximating Optimal Welfare in Complementary Allocation under Decentralized Information
AI总结：
研究分散信息下互补商品分配问题，提出阈值转介和阶梯报告机制，将局部信息导致的线性福利损失降至常数因子，实现近似最优福利。
AI中文摘要：
互补性资源通常由观察个体需求不同坐标的机构分配。如果一项干预需要互补资源，某机构可能知道该人是否缺乏自身资源；但不知道供应是否构成有用的组合。我们研究当每个机构仅观察基线访问配置的自身坐标时，m种可分割互补商品的分配问题。为将信息与激励分离，我们针对慷慨的分散基准DEC衡量这种分割的福利成本：该基准是在合作机构、已知总体分布和能力的情况下，仅依据局部信息行动的最佳规则。即便如此，仅局部观察就可能使最优协调政策任意低效：因子随m线性增长（即使能力相等），且因子与OPT成反比（仅三个机构时）。阈值转介可挽回大部分损失：机构报告其值是否低于公共阈值，清算规则仅使用联合报告。按报告聚合类型捕获最优半效用生存曲线下的矩形。我们的主要工具是轮廓级收费证明：若最优效用至少为阈值的两倍，则OPT在每个缺陷坐标上至少支付该值。这产生至少OPT/[4(1+ln(2/OPT))]的福利，每个机构一位；等收入族表明该对数损失对单阈值是紧的。几何阈值阶梯将此改进为OPT的常数分数，使用双对数消息：阶梯恢复OPT/8，使用Θ(loglog(1/OPT))位，且在该类内这是必要的。结果隔离了简单报告语言如何将大的局部信息损失转化为常数因子恢复。简言之：单阈值获得对数近似。阶梯，使用log-of-log位，获得常数因子。
英文摘要：
Complementary resources are often allocated by agencies that see different coordinates of an individual's needs. If an intervention requires complementary resources, an agency may know if said person lacks its own resource; yet not know if supplying completes a useful bundle. We study allocation of $m$ divisible complementary goods when each agency observes only its own coordinate of a baseline-access profile. To isolate information from incentives, we measure the welfare cost of this split against a generous decentralized benchmark DEC: the best rule that acts on local information alone, with cooperative agencies and known population distribution and capacities. Even so, local observation alone can make optimally coordinated policies arbitrarily inefficient: a factor linear in $m$ (even with equal capacities), and a factor inverse in OPT (with but three agencies). Threshold referrals recover much of this loss: an agency reports if its value lies below a public threshold, and a clearing rule uses only the joint reports. Aggregating types by their reports captures a rectangle under the optimal half-utility survival curve. Our main tool is a profile-level charging certificate: if optimal utility is at least twice a threshold, OPT pays at least that on every deficient coordinate. This yields welfare at least ${\rm OPT}/[4(1+\ln(2/{\rm OPT}))]$ with one bit per agency; and an equal-revenue family shows this log-loss tight for one threshold. A geometric threshold ladder improves this to a constant fraction of OPT with doubly-logarithmic messages: a staircase recovers ${\rm OPT}/8$ with $Θ(\log\log(1/{\rm OPT}))$ bits, and this is necessary within the class. The results isolate how a simple reporting language turns large local-info losses into constant-factor recovery. In short: One threshold gets a log-approximation. A staircase, with log-of-log bits, a constant-factor.
