ELEKTROTEHNIŠKI VESTNIK 78(5): 287-292, 2011 ENGLISH EDITION Game Theory Application for Performance Optimisation in Wireless Networks Erik Pertovt, Tomaž Javornik, Mihael Mohorčič Institut "Jožef Stefan", Jamova cesta 39, 1000 Ljubljana, Slovenija E-pošta: erik.pertovt@ijs.si Abstract. Game theory has been recently introduced in wireless network design as a powerful modeling and analysing tool for competitive and completely distributed environments. It is a well-suited to describe mutual conflicting situations between multiple devices which attempt to communicate through a shared medium. In order to demonstrate suitability of a game-theoretic approach for optimisation of wireless networks, we first present the main idea, concepts and components of game theory. We then provide mapping of principles between the areas of game theory and wireless networks, and present some applications of game theory in wireless networks. We develop and implement a model for transmit power control optimisation in a wireless relay network consisting of wireless sensor network coordinator nodes using the category of potential games. In the game, we determine the Pareto efficient Nash equilibrium, which represents the optimal stable operating point of the network. Keywords: game theory, wireless networks, relay network, potential games, optimisation 1 INTRODUCTION As wireless communication networks are becoming more and more extensive and complex, their performance optimisation and management with conventional deterministic methods are no longer possible. Therefore, besides heuristic methods, other approaches are being increasingly used for these purposes, game theory [1] as a special field of applied mathematics being also one of them. Game theory is a powerful tool to model situations where the success of an entity also depends on the decisions of other entities of the system. It can be used in the case when interests of one entity or group of entities intersect or influence over those of other entity or entities. Every intersection of interests is called a conflict situation [2] and represents a conflict between multiple entities present in the system. The behavior of participants in such conflict situation can be described by a mathematical model, which takes into consideration that actions or decisions made by participants obey certain rules. It is also assumed that participants act rationally [3], i.e., they always choose those actions which are promising the largest possible benefit, taking into consideration options of opponents and some external circumstances. Game theory being a discipline for modeling situations in which decision makers interact between each other, it is also well suited for the use in wireless communication systems. In these systems, the interaction between individual devices occurs due to the sharing of the radio channel. Assuming each device or node is capable of adapting independently utilizing game theory makes possible to steer the network to a stable operating point. The intention of this paper is to present game theory as one of the possible methods for optimisation of radio resources in wireless networks. To this end we first present the main idea, concepts and components of game theory. We describe application of game theory in wireless networks and link various concepts and components of game theory with corresponding wireless networks concepts and components. As an example of using game theory, a potential game, which is particularly suitable for use in wireless networks, is applied to model optimisation of a transmit power control in coordinator nodes of a multi-hop hierarchical wireless sensor network (WSN). 2 BASIC CONCEPTS OF GAME THEORY Game theory studies games in which result depends on the skills of players besides on pure chance. These games are called strategic games [4]. A game is actually a collection of rules and arrangements to be followed by players. A game consists of three basic components: a set of players, a set of strategies/actions for each player and a set of preferences over possible outcomes. The participants of the game are players, which choose their actions in each stage of the game. The choices of players always influence the resulting outcome of the game for each player, thus they also Received November 24, 2011 Accepted December 12, 2011