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With the spread of passive Radio Frequency Identification (RFID) systems, new applications will see the coexistence of more and more RFID readers in the same area. As for wireless devices, also RFID readers experience collisions whenever sharing the same communication channel. In this paper, an anti-collision protocol has been proposed in order to solve the reader collision problem. The aims of the proposed solution are: (1) to prevent and avoid collisions among readers; and (2) to limit the access delay of the readers on the channel, while guaranteeing them fairness with respect to the channel contention. The reader anticollision here proposed, referred as to High Fairness Reader Anti-Collision Protocol (HF-RACP), has been designed taking into account passive tags and their limitations in terms of computational and frequency selectivity capabilities. In this paper, after presenting the reader collision problem and discussing the simulation models and the evaluation methodology used herein, the simulation results for several anti-collision algorithms are shown in terms of collision avoidance and access delay. The comparison with contention-based schemes, like Listen Before Talk (LBT), demonstrates that HF-RACP is more effective against collisions, improves the fairness among readers and considerably reduces the maximum access delay.