Bernoulli Factories and Black-box Reductions in Mechanism Design

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