In this paper, we consider the amplify-and-forward relaying transmission in the downlink of a multi-channel cellular network with one base station and multiple relay-destination pairs. Spatial reuse of the relaying slot by allowing simultaneous transmissions from the relays is adopted to avoid the spectral loss incurred by the half-duplex relays. The relays are modeled as rational agents engaging in a non-cooperative game. In order to maximize its individual rate, each relay node iteratively allocates its power across different subchannels based on local information, while treating the signals from the other users as additive noise. First, we propose a distributed algorithm based on best response that is applicable in any signal to interference plus noise ratio (SINR) regions. Then, by focusing on the low SINR region, we propose a modified iterative water-filling algorithm. The existence of Nash equilibrium (NE) is guaranteed and the sufficient condition to reach a NE iteratively is de...