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Wireless Mesh Networks (WMNs) are multi hop networks in which the mesh clients rely on static mesh routers (or directly via other mesh clients) to relay data from one point to another in a multihop fashion. WMN gained significant attention because of the numerous applications it supports, e.g., broadband home networking, community and neighborhood networks, delivering video, building automation, in entertainment and sporting venues etc. But the main challenge of these multihop networks is the susceptibility to various security threats. In this paper, we address the problem of gray hole attack in which a malicious node refuses to forward a subset of the packets it receives. We present the attack in a simple network of mesh routers in the framework of a non-cooperative Markov game between genuine and malicious mesh router. The main objective of the legitimate node (Player I) is to maximize its throughput by minimizing the loss caused by the attackers. On the other hand , the main goal of the attacker (Player II) is to minimize the throughput of the network by dropping the data packets. We investigate the nash equilibrium of the non cooperative game by allowing the nodes to select their own actions that optimizes the individual performance in terms of the packet delivery ratio.