Bayesian Mechanism Design for Budget-Constrained Agents

TL;DR

This paper develops mechanisms for Bayesian settings with agents constrained by budgets, providing reductions to unconstrained problems and achieving constant factor approximations for welfare and revenue.

Contribution

It introduces general reductions from budget-constrained Bayesian mechanism design to unconstrained problems, enabling effective approximation solutions.

Findings

Constant factor approximations for welfare and revenue in budgeted settings

Extensions to private budgets with truthful reporting

Overcoming utility discontinuities caused by budgets

Abstract

We study Bayesian mechanism design problems in settings where agents have budgets. Specifically, an agent's utility for an outcome is given by his value for the outcome minus any payment he makes to the mechanism, as long as the payment is below his budget, and is negative infinity otherwise. This discontinuity in the utility function presents a significant challenge in the design of good mechanisms, and classical "unconstrained" mechanisms fail to work in settings with budgets. The goal of this paper is to develop general reductions from budget-constrained Bayesian MD to unconstrained Bayesian MD with small loss in performance. We consider this question in the context of the two most well-studied objectives in mechanism design---social welfare and revenue---and present constant factor approximations in a number of settings. Some of our results extend to settings where budgets are private and agents need to be incentivized to reveal them truthfully.