AI 中文总结
针对多买家异质物品的效用最大化问题，提出常数因子近似机制，利用价格与免费抽奖分离上界，实现多项式时间可计算的贝叶斯激励相容机制。
AI 中文摘要
受消费者以不可转让的代价支付的社会服务的启发，我们研究了在多个单位需求买家和异质物品环境下最大化消费者效用的机制，其中物品的价值独立地从已知的先验分布中抽取。先前在效用最大化方面的研究近似社会福利，并表明最优效用与社会福利之间的差距是对数级的。我们解决了简单机制能否保证对最优效用本身的常数因子近似的问题。我们的机制对于一般的独立价值实现了$(5.67+\varepsilon)$-近似，当价值是独立同分布时，改进到$2e/(e-1)<3.164$。每个买家从公布的物品价格或免费物品抽奖中选择他们最喜欢的选项，并且竞争解决决定哪些买家的请求被服务；这是贝叶斯激励相容的、事后个体理性的，并且可以在多项式时间内计算。我们的主要技术贡献是对最优事前约束效用的一个一般上界，该上界分离了公布价格和免费抽奖所捕获的贡献。这些结果为简单、近似收入最优机制的理论建立了效用的对应物。
英文摘要
Motivated by social services where consumers pay with non-transferable ordeals, we study mechanisms that maximize consumer utility for multiple unit-demand buyers and heterogeneous items whose values are drawn independently from known prior distributions. Prior work in utility maximization approximates social welfare and shows that the gap between optimal utility and social welfare is logarithmic. We resolve the question of whether simple mechanisms can guarantee a constant-factor approximation to optimal utility itself. Our mechanisms achieve a $(5.67+\varepsilon)$-approximation for general independent values, improving to $2e/(e-1)<3.164$ when values are i.i.d. Each buyer chooses their favorite option from posted item prices or free item lotteries, and contention resolution determines which buyers' requests are served; this is BIC, ex-post individually rational, and computable in polynomial time. Our main technical contribution is a general upper bound on the optimal ex-ante-constrained utility that separates the contributions captured by posted prices and free lotteries. These results establish a utility counterpart to the theory of simple, approximately revenue-optimal mechanisms.
Comments40 pages, including appendices
