We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multi-dimensional and continuous type spaces. The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanism’s output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility. We overcome this barrier by employing and generalizing the computational model in the literature on Bernoulli Factories . In a Bernoulli factory problem, one is given a function mapping the bias of an “input coin” to that of an “output coin,” and the challenge is to efficiently simulate the output coin given only sample access to the input coin. This is the key ingredient in designing an incentive compatible mechanism for bipartite matching, which can be used to make the approximately incentive compatible reduction of Hartline et al. [18] exactly incentive compatible.

中文翻译：

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机构设计中的伯努利工厂和黑盒简化

我们为福利最大化问题提供了从贝叶斯激励兼容机制设计到贝叶斯算法设计的多项式时间缩减。与先前的结果不同，我们的减少实现了对多维和连续类型空间问题的精确激励兼容性。在先前的黑盒减少中阻止精确激励兼容性的关键技术障碍是修复违反激励约束需要了解机制输出的分布，这通常是#P-hard to计算。通过抽样来估计输出分布的减少不可避免地会受到抽样误差的影响，这通常会排除精确的激励兼容性。我们通过使用和推广文献中的计算模型来克服这个障碍伯努利工厂. 在伯努利工厂问题中，给定一个函数，将“输入硬币”的偏差映射到“输出硬币”的偏差，挑战是在仅给定对输入硬币的样本访问的情况下有效地模拟输出硬币。这是为二分匹配设计激励相容机制的关键因素，可用于使 Hartline 等人的近似激励相容减少。[18] 完全激励兼容。