In this paper, we investigate the power allocation (PA) problem for two-way relay networks (TWRNs) with amplify-and-forward (AF) protocol. We propose a unified power allocation algorithm which can minimize average symbol error probability (SEP) and average outage probability while maximizing average sum rate in high signal to noise ratio (SNR) regions simultaneously. It is shown that the proposed algorithm has a closed-form solution which only depends on statistical channel knowledge. Simulation results show that the proposed scheme, although derived under the high SNR assumption, also works very well in low and medium SNR regions.