We propose a novel optimal time slot allocation scheme for clustered underwater acoustic sensor networks that leverages physical (PHY) layer information to minimize the energy consumption due to unnecessary retransmissions thereby improving network lifetime and throughput. To reduce the overhead and the computational complexity, we employ a two-phase approach where: (i) each member node takes a selfish decision on the number of time slots it needs during the next intra-cluster cycle by solving a Markov decision process (MDP), and (ii) the cluster head optimizes the scheduling decision based on the channel quality and an urgency factor. To conserve energy, we use a hybrid medium access scheme, i.e., time division multiple access (TDMA) for the intra-cluster communication phase and carrier sense multiple access with collision avoidance (CSMA/CA) for the cluster head-sink communication phase. The proposed MAC protocol is implemented and tested on a real underwater acoustic testbed using SM-75 acoustic modems by Teledyne Benthos. Simulations illustrate an improvement in network lifetime. Additionally, simulations demonstrate that the proposed scheduling scheme with urgency factor achieves a throughput increase of 28% and improves the reliability by up to 25% as compared to the scheduling scheme that neither use MDP nor optimization. Furthermore, testbed experiments show an improvement in throughput by up to 10% along with an improvement in reliability.