This paper analyzes Game Theory (GT) from the point of view of moral psychology and makes explicit some of its assumptions regarding the human person as a moral agent, as well as the ends of human action, and reciprocity. Using a largely philosophical methodology, we will argue that GT assumes an instrumental form of rationality underpinned by a logic of self-interest, hence placing individuals, communities, and their social practices in service of external goods and their maximization. Because of this, GT is not adequate to describe the entirety of human social existence and interaction. Nevertheless, by revealing these assumptions, GT can be amplified with another form of rationality based on realist ethics and a personalist anthropology reinforced by the logic of gift. This rationality values the singularity of each person as a holistic unity, as the center of the social realm and as an end in herself called to growth and flourishing with others, nurturing the human community through giving and receiving. We will thus provide a wider philosophical framework for GT with a series of non-mathematical axioms of what can be called a Game Metatheory (GMt). These axioms refer to society as a complex system, not to particular interactions. GMt axioms are not a model of social games, but rather an axiomatic description of social life as a game, revealing its systematic character, complexity, and possible deterioration.