Mesh Wireless Local Area Network (WLAN) is a promising access network to enhance channels utilization, extend access coverage with simple and cheap network components. Power management affects mesh WLAN network coverage, topology, throughput, traffic routing and end to end delay. In this paper, power management problem is formulated to show its impact on mesh WLAN network throughput. Then this formulation is used to propose a new ranking based cooperative game strategy. The proposed ranking of each access point depends on its cell congestion factor, number of hops to the gateway and SINR. This game strategy objective is to maximize the network average user's data rate with considering mesh WLAN implementation requirements. Results show that the proposed strategy achieves higher average user's data rate than non-cooperative game Nash equilibriums and comparable result with the optimum power assignment.