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Power control in wireless sensor networks is vital to maintain reliable communication links and to maximize the battery life. Transmitting at high power not only reduces the lifetime of the nodes and that of the network, but it also introduces excessive interference. Hence it is essential for each node to transmit at minimal transmit power, thereby reducing interference and maintaining network connectivity. This paper analyses a game theoretic model taking into consideration the residual energy of the nodes in a homogenous wireless sensor network considering random and square topology. The utility function of nodes that minimizes power consumption is analysed and the existence of Nash Equilibrium is studied. Simulation results show that, power consumption is reduced and throughput is maintained when square topology is considered. I. INTRODUCTIONireless sensor network (WSN) is a wireless network composed of large number of low cost, low power sensor nodes deployed either inside or very close the event, each of which is capable of sensing the physical environment for data acquisition, computation of data and communication [1]. One of the desired features of wireless sensors networks is their capability to function unattended in harsh environments and inaccessible terrains in which contemporary monitoring schemes are unsafe, heavyhanded, and sometimes infeasible. Many sensor network applications like habitat monitoring, civil structure monitoring, surveillance etc., require long lifetime ranging from several months to years. WSN has a high density of nodes, high malfunction rate of nodes; possess limited power supply powered by batteries, limited computing capability and data storage capacity and the topology of the network changes frequently. Since the nodes are deployed in hostile environment it is not feasible to replace the batteries. Therefore energy conservation is very crucial for WSNs, both for each sensor node and the entire network level operations to prolong the network lifetime. Since radio communication is the major source of energy consumption in WSNs, topology control mechanisms are fundamental to achieving good network energy efficiency.Topology control has been studied comprehensively in the past years [2]. The purpose is to control the topology of the graph representing the communication links between R.Valli is the Research Scholar,

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