Bayesian Budget Feasibility with Posted Pricing

TL;DR

This paper develops simple posted pricing mechanisms for Bayesian budget feasible mechanism design, achieving near-optimal value approximation while ensuring ex post budget balance, with applications in crowdsourcing platforms.

Contribution

It introduces practical posted pricing mechanisms that approximate Bayesian optimal mechanisms with ex post budget balance for additive and submodular valuations.

Findings

Mechanisms are simple and practical for real-world applications.

Achieve near-optimal value approximation in Bayesian settings.

Ensure ex post budget balance in posted pricing schemes.

Abstract

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).