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A hierarchical slotted aloha game

We consider in this paper a wireless system composed of one central receiver and several selfish transmitters communicating via the slotted aloha protocol. We study a noncooperative hierarchical system based on the Stackelberg game concept. Each user of our game tends to maximize his own throughput or minimize his expected delay of backlogged packets depending on his transmission probability and transmission probabilities of other users in the network. Using a 4D Markovian model, we compute the steady state of the system and derive the average throughput and expected delay. We then investigate the impact of introducing hierarchy in the random access protocol. Later, exhaustive performance evaluations were carried out, we show that the global performance of the system is improved compared to slotted aloha system without hierarchy. However, a not sharp performances slow-down may be observed for the followers when the number of users is not large, but they turn to outperform Nash equilibrium under average and heavy load.