A game is an efficient model of interactions between agents, for the following basic reason: the players follow fixed rules, have interests on all possible final outcomes of the game, and the final result for them does not depend only from the choices they individually make, but also from the choices of other agents. Thus the focus is actually on the fact that in a game there are several agents interacting. In fact, more recently this theory took the name of Interactive Decision Theory. It is related to classical decision theory, but it takes into account the presence of more than one agent taking decisions. As we shall constantly see, this radically changes the background and sometimes even the intuition behind classical decision theory. So, in few words, game theory is the study of taking optimal decisions in presence of multiple players (agents). Thus a game is a simplified, yet very efficient, model of real life every day situa- tions. Though the first, and probably more intuitive, applications of the theory were in an economical setting, theoretical models and tools of this theory nowadays are spread on various disciplines. To quote some of them, we can start from psychology: a more modern approach than classical psychanalysis takes into account that the hu- man being is mainly an interactive agent. So to speak, we play everyday with our professors/students, with our parents/children, with our lover, when bargaining with somebody. Also the Law and the Social Sciences are obviously interested in Game Theory, since the rules play a crucial role in inducing the behaviour of the agents. Not many years after the first systematic studies in Game Theory, interesting ap- plications appeared to animals, starting with the analysis of competing species. It is much more recent and probably a little surprising to know that recent applications of the theory deal with genes in microbiology, or computers in telecommunication problems. In some sense, today many scholars do believe that these will be the more interesting applications in the future: for reasons that we shall constantly see later, humans in some sense are not so close to the rational player imagined by the theory, while animals and computers "act" in a more rational way than human beings, clearly in an unconscious yet efficient manner.