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Underwater Acoustic Sensor Networks (UW-ASNs) consist of a variable number of sensors and vehicles that are deployed to perform collaborative monitoring tasks over a given area through collecting monitored data or data streams. Detecting bursts in data streams of UW-ASNs is an important area of research with a wide range of applications. In this paper, we build semi-autonomous underwater acoustic sensor networks based on Peer-to-Peer (P2P) technology for sharing various UW-ASNs' information. In addition, we propose a novel approach for solving the problem of elastic burst detection in UW-ASNs based on evolutionary game theory. Extensive experiments have been carried out to assess the performance of the proposed method. The obtained results show that our burst detection method performs better than existing method with different data distributions.