We consider a two-way relay network where a relay helps two source nodes exchange information using the time division broadcast protocol. Two power allocation schemes are presented: the first one is to minimize the maximum outage probability of the two traffic flows with the power constraint and the second one is to minimize the total transmit power of the three nodes with the outage probability constraints. We use the Karush-Kuhn-Tucker (KKT) conditions to determine the optimum power allocation for both schemes. The simulation results confirm that the proposed power allocation schemes have better performance than the conventional schemes.