International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-6 Issue-3, February 2017 5 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Pvt. Ltd. Abstract: Game Theory approaches and their application in improving the performance of Wireless sensor networks (WSNs) are discussed in this paper. The mathematical modeling and analysis of WSNs may have low success rate due to the complexity of topology, modeling, link quality and etc, however Game Theory is a field, which can efficiently used to analyze the WSNs. Game theory is related to applied mathematics that describes and analyzes interactive decision situations. Game theory has the ability to model independent, individual decision makers whose actions affect the surrounding decision makers. The outcome of Complex interactions among rational entities can be predicted by a set of analytical tools, however the rationality demands a stringent observance to a strategy based on measured of perceived results. Researchers are adopting game theory approaches to model and analyze leading wireless communication networking issues, which includes QoS, power control, resource sharing and etc. Index Terms: Wireless sensor network; Game Theory; Cooperative game theory; Non-cooperative game theory; Wireless communications. I. INTRODUCTION The roots of Game theory are very old and the thoughts behind game theory have appeared in history [5], apparently in the holy books, the writings of Charles Darwin and etc [7]. However, there are some arguments on Daniel Bernoulli, that the first study of game theory was done by him i.e., the “Bernoulli’s Principles”[8] and other argument is that the first mathematical analysis tool was presented by Thomas Bayes, known as “Bayes ‘Theorem”. The basis of modern game theory is development of a three determining works; a nash equilibrium, a competitive equilibrium and a mixed strategy [9]. Now, we can say that “Game Theory” is not a new concept. However, the concept has not yet been fully established and it limits the application to special conditions only [1]. II. GAME THEORY Game theory is defined as a collection of mathematical models formulated to study situations of conflict and cooperation. It results into finding the best measures for individual decision makers in these situations and recognizing stable outcomes. The object of study in game theory is the game, defined to be any situation in which: Revised Version Manuscript Received on January 19, 2017. M. Shoukath Ali, Research Scholar, Department of Electronics & Communication Engineering, Sri Satya Sai University of Technology & Medical Sciences, Sehore (Madhya Pradesh). India. Dr. R.P. Singh, Vice-Chancellor, Professor, Department of Electronics & Communication Engineering, Sri Satya Sai University of Technology & Medical Sciences, Sehore (Madhya Pradesh). India.  There are at least two players: A player may be a wireless node, individual, a nation, a company or even a biological species.  Each player has a number of courses of strategies and possible actions, he/ she may choose to follow.  The outcome of game is decided by the strategies chosen by each player. John Nash (1950) demonstrated that finite games always have a strategic equilibrium (also called a nash equilibrium). Nash equilibrium is a list of actions one for each player. To get a better payoff, no player can unilaterally change his/her strategy. This concept is referred as non-cooperative game theory III. ASSUMPTIONS AND TERMINOLOGIES The different terminologies of the game theory are now defined. 1. Players: Decision making in the game is done by the players. If there are two players in a game and if the players are two organizations (for e.g. organization R and organization S) competing for tenders, trade gain in a country by two other countries, two persons bidding in a game, etc. 2. Strategy: It is action taken by a player in a game, for e.g., giving furniture free of cost, giving additional discount on additional hardware, special prize, etc. In strategic form of game, a strategy is one of the given possible actions of a player. In an extensive game, a strategy is a complete map of choices, one for each of the player. Further, the strategy can be classified into mixed strategy and pure strategy. Let m be the strategies of player R and n be strategies of player S, P i be the probability of selection of the alternative i of player R, i = 1,2,3,….m. Let Q j be the probability of selection of the alternative j of player S, for j = 1, 2, 3…..n. The sum of the probabilities of range of various alternatives of each of the players is equal to equation as shown below (i)Pure strategy: If a player uses a particular strategy with a probability of 1, then that is a pure strategy. This means if player R follows a pure strategy, then only one of the P i values will be equal to 1 and the remaining P i values will be equal to 0. A set of probabilities of selection of the alternatives for player R is shown below: P 1 = 0, P 2 =1, P 3 = 0. The sum of these probabilities is equal to 1.That is p 1 + p 2 + p 3 =0+1+0=1. (ii)Mixed strategy: In this, a player follows more than one strategy. But the probability of selection of the individual strategies will be less than one and their sum will be equal to one. Q 1 = 0.65, Q 2 =1, Q 3 = 0.35 The sum of these probabilities is equal to 1.That is p 1 + p 2 + p 3 =0.65+1+0.35=1. A Study on Game Theory Approaches for Wireless Sensor Networks M. Shoukath Ali, R. P. Singh