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High false alarm rate in intensive care units (ICUs) has been identified as one of the most critical medical challenges in recent years. This often results in overwhelming the clinical staff by numerous false or unurgent alarms and decreasing the quality of care through enhancing the probability of missing true alarms as well as causing delirium, stress, sleep deprivation and depressed immune systems for patients. One major cause of false alarms in clinical practice is that the collected signals from different devices are processed individually to trigger an alarm, while there exists a considerable chance that the signal collected from one device is corrupted by noise or motion artifacts. In this paper, we propose a low-computational complexity yet accurate game-theoretic feature selection method which is based on a genetic algorithm that identifies the most informative biomarkers across the signals collected from various monitoring devices and can considerably reduce the rate of false alarms.