Vol. 2, Issue 12, Part I (2016)

Abstract
In this paper, we attempted a glimpse at the fascinating field of Algorithmic Game Theory. This is a field that is currently undergoing a very intense investigation by the community of the Theory of Computing. Although some fundamental theoretical questions have been resolved (for example, the complexity of computing Nash equilibria for 2-player games), there are still a lot of challenges ahead of us. Among those, most important are, in our opinion, the further complexity classification of algorithmic problems in Game Theory, and the further application of systematic techniques from Game Theory to modeling and evaluating modern computer systems. The resulting equations and inequalities define polytopes, whose “completely labeled” vertex pairs are the Nash equilibria of the game. Extensive games are game trees, with information sets that model imperfect information of the players.