The rapid development of IoMT facilitates pervasive healthcare networks. However, numerous MUs lead to deficient wireless channel and computation resources. Edge computing based healthcare system is appreciated as a satisfactory paradigm to solve this obstacle. Based on the physical bound of WBANs, the IoMT is separated into two sub-networks, that is, intra- WBANs and beyond-WBANs. Considering the characteristics of healthcare systems, the cost of MUs relies on medical urgency, AoI and energy dissipation. In intra-WBANs, the wireless channel resource allocation problem is modeled by a cooperative game. The Nash bargaining solution is utilized to obtain the unique Pareto optimal point. In beyond-WBANs, MUs are considered to be rational and potentially selfish. Thus, a non-cooperative game is formulated to minimize the system-wide cost. To demonstrate the effectiveness of our proposed solution, performance evaluations are conducted with respect to the system-wide cost and the number of MUs benefiting from edge computing. Finally, several research challenges and open issues are discussed for further work.