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In this paper, we formulate multi-channel assignment in Wireless Sensor Networks (WSNs) as an optimization problem and show it is NP-hard. We then propose a distributed Game Based Channel Assignment algorithm (GBCA) to solve the problem. GBCA takes into account both the network topology information and transmission routing information. We prove that there exists at least one Nash Equilibrium in the channel assignment game. Furthermore, we analyze the sub-optimality of Nash Equilibrium and the convergence of the Best Response in the game. Simulation results are given to demonstrate that GBCA can reduce interference significantly and achieve satisfactory network performance in terms of delivery ratio, throughput, channel access delay and energy consumption.