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In this paper we study a two access point (AP) providers' price competition in a wireless mesh network (WMN). The two AP providers offer IP-based service for possibly different prices and quality-of-service (QoS) in terms of mean packet delay. The end-users' choice between the APs is based on their compensated utility. We consider a two stage game among the two AP providers and their end-users. In stage 1, the AP providers set their prices to maximize their proiquestts respectively. In stage 2, given the prices and QoS offered by both AP providers, the end-users decide which AP to seek service from or opt out of both APs. Then the game returns to stage 1, in which both AP providers adjust their optimal prices based on the decisions of the end-users to seek equilibrium among themselves and their end-users. With this game theoretical approach, we develop an analytical framework to find the Nash equilibrium points from which two APs and end-users would not move from.