Wireless sensor network has large number of low-cost tiny nodes with sensing capability. These provide low cost solutions to many real world problems such as such as defence, Internet of things, healthcare, environment monitoring and so on. The sensor nodes of these networks are placed in vulnerable environment. Hence, the security of these networks is very important. Intrusion Detection System (IDS) plays an important role in providing a security to such type of networks. The sensor nodes of the network have limited power and, traditional security mechanisms such as key-management, encryption decryption and authentication techniques cannot be installed on the nodes. Hence, there is a need of special security mechanism to handle the intrusions. In this paper, intrusion detection system is designed and implemented using game theory and machine learning to identify multiple attacks. Game theory is designed and used to apply the IDS optimally in WSN. The game model is designed by defining the players and the corresponding strategies. Quantal Response Equilibrium (QRE) concept of game theory is used to select the strategies in optimal way for the intrusion's detection. Further, these intrusions are classified as denial of service attack, rank attack or selective forwarding attacks using supervised machine learning technique based on different parameters and rules. Results show that all the attacks are detected with good detection rate and the proposed approach provides optimal usage of IDS.