We propose to move towards a risk-profiling approach to determine inspection strategies, with the aim of targeting audit of buildings that have a higher chance of being problematic. Historical data suggests that compliance of responsible persons (those in charge of ensuring fire safety at a particular dwelling) is an important factor in likelihood of danger, but it is presently overlooked in inspection models. With the goal of incorporating compliance in decisions of what and when to inspect, we construct game theoretic models for inspections, encompassing compliance likelihood of responsible persons. The (action-based) game theoretic representations serve to enable the construction of combinatorial optimization algorithms (algorithms for finding the optimal solution to problems where exhaustive searches are an impossibility), capable of deliberative search to identify optimal sequences of inspections. This paper presents a case study on Compliance, some statistical findings, then followed by the conceptual game-theoretical modeling.