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In this paper, we investigate the optimal design of cooperative network-coded strategies for a three-node wireless network with time-varying, half-duplex erasure channels. To this end, we formulate the problem of minimizing the total cost of transmitting M packets from source to two receivers as a Markov Decision Process (MDP). The actions of the MDP model include the source and the type of transmission to be used in a given time slot given perfect knowledge of the system state. The cost of packet transmission is defined such that it can incorporate the difference between broadcast and unicast transmissions, e.g., in terms of the rate of packet transmission or the energy consumption. A comprehensive analysis of the MDP solution is carried out under different network conditions to extract optimal rules of packet transmission. Inspired by the extracted rules, we propose two near-optimal heuristics that are suitable for practical systems. We use two wireless channel models to analyse the performance of the proposed heuristics in practical wireless networks, namely, (a) an infrastructure-to-vehicle (I2V) communication in a highway scenario considering Rayleigh fading, and (b) real packet loss measurements for WiFi using Aalborg University’s Raspberry Pi testbed. We compare our results with random linear network coding (RLNC) broadcasting schemes showing that our heuristics can provide up to 2x gains in completion time and up to 4x gains in terms of reliably serviced data packets.