In Bayesian mechanism design, a strong assumption is that the distributions of the players' private types are common knowledge to the designer and the players ---the common prior assumption. An important problem that has received a lot of attention in both economics and computer science is to repeatedly weaken this assumption in game theory ---the “Wilson's Doctrine”. In this work we consider, for the first time, multi-item auctions where the knowledge about the players' value distributions is arbitrarily scattered among the players and the seller. Each one of them privately knows some of the value distributions or a refinement of them, no constraint is imposed on who knows which distributions, and the seller does not know who knows what. In such an unstructured information setting, we design mechanisms for unit-demand auctions and additive auctions, whose expected revenue approximates that of the optimal Bayesian mechanisms by “crowdsourcing” the players' and the seller's knowledge. In some sense, our results show that the common prior assumption is without much loss of generality in Bayesian auctions if one is willing to give up a fraction of the revenue, and this fraction shrinks gracefully as the amount of knowledge in the system increases.
Jing Chen is an Assistant Professor in the Computer Science Department at Stony Brook University. She is also an Affiliated Assistant Professor in the Economics Department and an Affiliated Member of the Stony Brook Center for Game Theory. Her major research interests are computational game theory, mechanism design, auctions, healthcare, and markets. Jing received her PhD in Computer Science from MIT, and her M.E. and B.E. from Tsinghua University. Before joining Stony Brook in 2013, she did a one-year postdoc at the School of Mathematics in the Institute for Advanced Study, Princeton. She received the NSF CAREER Award in 2016 for her research on mechanism design.