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However, the distributed estimation in autonomous clustered WSNs faces a vital problem of sensors\u2019 selfishness. Each sensor autonomously decides whether or not to transmit its observations to the fusion center (FC) and not be controlled by the fusion center (FC) any more. Thus, to encourage cooperation within selfish sensors, infinitely and finitely repeated games are firstly modeled to depict sensors\u2019 behaviors. Then, the existences of Nash equilibriums for infinitely and finitely repeated games are discussed. 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