贝叶斯最优机制设计中的随机性能力
The power of randomness in Bayesian optimal mechanism design
摘要：
我们调查的权力随机性的背景下，一个基本的贝叶斯最优机制设计问题-一个单一的卖方的目标是最大限度地提高预期收入分配多种资源的“单位需求”代理商的偏好从一个已知的分布。当代理人的偏好是一维时，Myerson的开创性工作[Myerson '81]表明随机性没有任何好处-最佳机制总是确定性的。在多维的情况下，每个代理的偏好由每个可用服务的不同值给出，Briest等人[Briest，Chawla，Kleinberg和Weinberg '10]最近表明，即使当单个代理仅提供4个服务时，通过最优随机机制和最优确定性机制获得的预期收入之间的差距也是无限的。然而，这种巨大的差距是通过不自然的实例来实现的，在这些实例中，不同服务的代理的值以特定的方式相关。我们表明，当代理的值不涉及相关性或特定类型的正相关性，随机性的好处只是一个小的常数因子（分别为4和8）。我们的正相关价值模型（我们称之为附加价值）是单位需求代理和替代品的自然模型。我们的研究结果扩展到多个代理设置以及。
英文摘要：
We investigate the power of randomness in the context of a fundamental Bayesian optimal mechanism design problem--a single seller aims to maximize expected revenue by allocating multiple kinds of resources to "unit-demand" agents with preferences drawn from a known distribution. When the agents' preferences are single-dimensional Myerson's seminal work [Myerson '81] shows that randomness offers no benefit--the optimal mechanism is always deterministic. In the multi-dimensional case, where each agent's preferences are given by different values for each of the available services, Briest et al. [Briest, Chawla, Kleinberg, and Weinberg '10] recently showed that the gap between the expected revenue obtained by an optimal randomized mechanism and an optimal deterministic mechanism can be unbounded even when a single agent is offered only 4 services. However, this large gap is attained through unnatural instances where values of the agent for different services are correlated in a specific way. We show that when the agent's values involve no correlation or a specific kind of positive correlation, the benefit of randomness is only a small constant factor (4 and 8 respectively). Our model of positively correlated values (that we call additive values) is a natural model for unit-demand agents and items that are substitutes. Our results extend to multiple agent settings as well.
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