基于差分隐私的近似最优机制设计
Approximately Optimal Mechanism Design via Differential Privacy
摘要：
在本文中，我们研究了在一个抽象的相互依赖的价值观模型和任意的目标函数的实施挑战。我们设计了一种机制，允许近似最优实现不敏感的目标函数在事后纳什均衡。此外，如果值是私有的，那么同样的机制就是策略证明。我们将我们的结果转换为两个特定的模型：定价和设施位置。我们设计的机制是最佳的添加剂因子的数量级的平方根的代理商，不涉及效用转移。我们的机制是两个辅助机制之间的彩票：以高概率，我们启动一个机制，减少玩家对社会选择的影响，同时选择最佳结果的概率高。这就是最近的差分隐私概念被采用的地方。有了互补概率，我们启动了一个通常远非最优但激励相容的机制。关节机制继承了两者所需的属性。
英文摘要：
In this paper we study the implementation challenge in an abstract interdependent values model and an arbitrary objective function. We design a mechanism that allows for approximate optimal implementation of insensitive objective functions in ex-post Nash equilibrium. If, furthermore, values are private then the same mechanism is strategy proof. We cast our results onto two specific models: pricing and facility location. The mechanism we design is optimal up to an additive factor of the order of magnitude of one over the square root of the number of agents and involves no utility transfers. Underlying our mechanism is a lottery between two auxiliary mechanisms: with high probability we actuate a mechanism that reduces players' influence on the choice of the social alternative, while choosing the optimal outcome with high probability. This is where the recent notion of differential privacy is employed. With the complementary probability we actuate a mechanism that is typically far from optimal but is incentive compatible. The joint mechanism inherits the desired properties from both.
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