Incentives are a key facet of human studies research, yet the state-of-the-art often designs and implements incentive systems in an ad-hoc, on-demand manner. We introduce the first vocabulary for formally describing incentive systems and develop a software infrastructure that enables UI-based graphical generation of complex, auditable, reliable, and reproducible incentive systems. We call this infrastructure the Open INcentive Kit (OINK). A review of recent literature from several communities finds that of the one hundred and twenty-one publications that incorporate incentives, only thirty-one describe their incentive system in detail, and all of these could be implemented using OINK. We evaluate OINK in practice by using it for an active energy monitoring deployment in Ghana and find that OINK successfully facilitates thousands of individual incentive payments. Finally, we describe our efforts to generalize OINK for different research communities, specifically focusing on architectural decisions around extensibility to support unanticipated use cases. OINK is free and open-source software.