In this paper, we study two-way relay networks (TWRNs) in which two source nodes exchange their information via a relay node indirectly in Rayleigh fading channels. Both Amplify-and-Forward (AF) and Decode-and-Forward (DF) techniques have been analyzed in the TWRN employing a Markov chain model through which the network operation is described and investigated in depth. Automatic Repeat-reQuest (ARQ) retransmission has been applied to guarantee the successful packet delivery. The bit energy consumption and goodput expressions have been derived as functions of transmission rate in a given AF or DF TWRN. Numerical results are used to identify the optimal transmission rates of which the bit energy consumption is minimized or the goodput is maximized. The network performances are compared in terms of energy and transmission efficiency in AF and DF modes.