Airport slot allocation is a combinatorial allocation problem (CAP) involving different complex and autonomous systems. Nowadays, the slots are allocated in a two-stage process: primary allocation is performed according to a set of administrative rules and for each airport independently, while secondary allocation is based on trading mechanisms. Several studies have raised inefficiencies in these processes. To enhance the airport slot allocation, this work proposes the study of the problem from a System of Systems Engineering approach (SoSE), both for the primary and secondary scenarios. Through the application of Auction Engineering and Experimental Economics, a set of market mechanisms is proposed to engineer these SoS. This paper presents their high-level formalisation, that will be implemented in future works and assessed according to a set of pre-established key performance indicators.