The aim of this chapter is to address the role of a novel concept in wireless telecommunications: Game theory. Game theory is a branch of applied mathematics, which has recently drawn attention as a powerful tool to solve complex problems in wireless environments. To fulfil the intended goal, this chapter introduces the most relevant concepts of game theory such as game, player, and strategy, and give an overview of the applications of game theory in wireless networks.
Game Theory For Wireless Communications
Why may game theory be applied to wireless telecommunications? The answer to this question rests on the very nature of game theory. It formalizes the interaction among autonomous agents (players) with selfish and even opposite objectives, and defines what a solution to the stated problem may be. It is clear then that by means of game theory the design and configuration of wireless networks such as ad hoc, sensor and mesh networks may be addressed in order to cope with limitations as power constraint, decentralized operation, interference mitigation and efficient multi-hop routing.
Game-theoretic concepts have mostly been applied in wireless applications to design network layer, flow control mechanisms and routing algorithms. Game theory has also demonstrated its validity for power allocation problem in wireless networks, where the network (e.g. the base station in centralized configurations) allocates the available resource (power) to the players (transmitters) with different types of constraints, e.g. interference, energy minimization or minimum required bit-rate constraints. In a similar manner, bandwidth allocation problems may be solved for this type of networks considering constraints such as the mutual interference among the transmitters. An alternative approach to obtaining solutions in telecommunication networks, e.g. routing protocols, is the usage of pricing: pricing schemes charge each node or customer locally for the resources he has used. An overview of the most relevant works on these areas is developed in the next section.
PHYSICAL (PHY) LAYER and medium access control (MAC) sublayer problems in wireless networks have not received too much attention up to recent dates in the context of game theory. For instance, in the case of PHY layer, we may consider cooperative diversity (explained in detail in a subsequent section) as a suitable technique to be studied applying game theory given the intrinsic selfish behaviour of the users of the network. With respect to the MAC sublayer, in addition to allocation applications, some game theoretic approaches have attempted to model packet radio protocols (Aloha, Slotted-Aloha) and channel assignment strategies. These applications demonstrate how promising game theory is for PHY and MAC LAYERS design.
Game theory, as we mentioned in the introduction, is a mathematical tool, but it is not very familiar to telecommunications. Hence, we will devote the remaining of this section to introduce the most relevant concepts and elements used in the literature up to now to address wireless systems by means of game theory. Although we consider the overview provided in this section adequate for the comprehension of the rest of this chapter, the reader may find it useful to complement this introduction to game theory with (MacKenzie and DaSilva, 2006).
Key Terms in this Chapter
Player: A decision-maker in the game-theoretic framework.
Game Theory: It is a branch of applied mathematics that is often used in the context of economics, which studies interactions between decision-makers.
Wireless: It refers to any type of electrical or electronic operation that is accomplished without the use of a wired connection.
Utility Function: Function associated to each player of a game which maps the resource consumption into a number so as to represent player’s preference.
Strategy: The different choices or alternative actions a player has to play a game.
Game: Mathematical formulation where the players choose strategies that will maximize their benefit.