Allocation for Social Good: Auditing Mechanisms for Utility Maximization

We consider the problem of a nonprofit organization ("center") that must divide resources among subsidiaries ("agents"), based on agents' reported demand forecasts, with the aim of maximizing social good (agents' valuations for the allocation minus any payments that are imposed on them). We investigate the impact of a common feature of the nonprofit setting: the center's ability to audit agents who receive allocations, comparing their actual consumption with their reported forecasts. We show that auditing increases the power of mechanisms for utility maximization, both in unit-demand settings and beyond: in unit-demand settings, we consider both constraining ourselves to an allocation function studied in past work and allowing the allocation function to vary; beyond unit demand, we adopt the VCG allocation but modify the payment rule. Our ultimate goal is to show how to leverage auditing mechanisms to maximize utility in repeated allocation problems where payments are not possible; we show how any static auditing mechanism can be transformed to operate in such a setting, using the threat of reduced future allocations in place of monetary payments.