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The overall performance of a cooperative relaying system largely depends on power allocation schemes. In this paper, we address the power allocation problem in a network-coded multiuser two-way relaying network, where multiple pair users communicate with their partners via a common relay node, and compete for the transmit power of the relay. An auction-based power allocation scheme is proposed, in which two users in each pair bid as a single player for a maximum utility of the whole pair, and share the total pair payment in proportion to the amount of power they obtained. The convergence of the proposed auction game (i.e., the convergence to a unique Nash Equilibrium) is theoretically proved by using a standard function. Moreover, the outage behavior is systematically analyzed and a closed form of the pair outage probability is derived. Finally, the performance of the proposed scheme is verified by simulation results.