Only very recently our community has acknowledged that the benefit of Structural Health Monitoring (SHM) can be properly quantified using the concept of Value of Information (VoI). The VoI is the difference between the utilities of operating the structure with and without the monitoring system. Typically, it is assumed that there is one decision maker for all decisions, i.e. deciding on both the investment on the monitoring system as well as the operation of the structure. The aim of this work is to formalize a rational method for quantifying the Value of Information when two different actors are involved in the decision chain: the manager, who makes decisions regarding the structure, based on monitoring data; and the owner, who chooses whether to install the monitoring system or not, before having access to these data. The two decision makers, even if both rational and exposed to the same background information, may still act differently because of their different appetites for risk. To illustrate how this framework works, we evaluate a hypothetical VoI for the Streicker Bridge, a pedestrian bridge in Princeton University campus equipped with a fiber optic sensing system, assuming that two fictional characters, Malcolm and Ophelia, are involved: Malcolm is the manager who decides whether to keep the bridge open or close it following to an incident; Ophelia is the owner who decides whether to invest on a monitoring system to help Malcolm making the right decision. We demonstrate that when manager and owner are two different individual, the benefit of monitoring could be greater or smaller than when all the decisions are made by the same individual. Under appropriate conditions, the monitoring VoI could even be negative, meaning that the owner is willing to pay to prevent the manager to use the monitoring system.