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Feedback implosion is a major problem limiting scalability in multicast satellite networks that arises when a large number of users transmit their feedback messages (FBMs) through the uplink channel, occupying a significant portion of system resources. This paper investigates how suppression of FBMs may be achieved through a novel feedback suppression scheme in which each user unilaterally decides whether to send a FBM or not. The users decisions are modeled applying game theory with inaccurate information. For this problem, the Bayesian equilibrium for the two and N-player game is investigated. It is proved that the feedback suppression game has a unique Bayesian equilibrium point. Then, based on appropriate numerical and simulation results, it is demonstrated that the proposed scheme avoids feedback implosion while at the same time it keeps feedback latency at very low levels. Finally, it is shown that the proposed scheme exhibits a significant performance improvement compared to existing exponential timer-based schemes.