  We consider the problem of budget feasible mechanism design proposed by
Singer (2010), but in a Bayesian setting. A principal has a public value for
hiring a subset of the agents and a budget, while the agents have private costs
for being hired. We consider both additive and submodular value functions of
the principal. We show that there are simple, practical, ex post budget
balanced posted pricing mechanisms that approximate the value obtained by the
Bayesian optimal mechanism that is budget balanced only in expectation. A main
motivating application for this work is the crowdsourcing large projects, e.g.,
on Mechanical Turk, where workers are drawn from a large population and posted
pricing is standard. Our analysis methods relate to contention resolution
schemes in submodular optimization of Vondrak et al. (2011) and the correlation
gap analysis of Yan (2011).
