The Theory of Expected Utility is the central theory that describes the way individuals make a decision according to the classical economic theory. Despite the fact of that, experimental studies on individuals' behavioral attitude of the last 20 years have shown that this theory does not accurately represent human behavior from a descriptive point of view. On the contrary, these studies bear out that reciprocity is the motivational drive of human decisions. People have a reciprocal behavior if they praise and repay good deeds and punish unkind ones. On the other hand, they are rational if they make every effort to maximize the benefit and their utility. In this review paper, we present a theoretical framework of reciprocity's measuring through the experimental economics. In particular, we propose an experimental way of identifying the incentives under which the subjects make a decision. Are they motivated by other people's well-being or by material self-interest? For achieving this, Homo Economicus and Homo Reciprocans ''conflict'' amid two different games of Game Theory. These games (Ultimatum Game and Dictator Game) create a new one, which is called ''The Reciprocity Game'' and it is going to offer us an important theoretical basis for the empirical measurement of human reciprocity in the future.