In these days the wireless communication is the most rapidly growing sector of information technology. The daily use of cellphones, wireless routers and Bluetooth devices became natural in developed countries. Unfortunately, the electromagnetic spectrum is a finite resource, so that we have to utilize it as effectively as possible. Therefore, one of the biggest challenges nowadays is to optimally distribute these forthcoming resources among the network participants. Beyond frequency allocation in the physical layer, we can find solutions for this problem in the MAC (Medium Access Control) layer, in which the game theory seems to be a very useful mathematical tool.
In my thesis at first I review the question of medium access in case of wireless networks. I will introduce the basic MAC protocols, and compare them considering their throughput efficiency. Afterwards we briefly examine the game theory, as a mathematical discipline which is often used for solving strategical conflicts. I show several telecommunication-related situations in order to illustrate the multiple application of game theory. In the third part of the paper I present the Aloha system, which is one of the oldest MAC protocols, and mainly used for wireless services. Thanks to its simplicity we can easily study the most important network parameters with the help of a mathematical model. In the last major chapter I make an attempt to create an algorithm with game theory considerations, which helps the slotted Aloha users to reach the maximum throughput efficiency. By the help of MATLAB simulations we will see how this new protocol corresponds to requirements such as fairness or scalability.