Game Theory is a rather vast discipline, the purpose of which is to analyze the strategic behaviors of decision-makers (players), or to study the situations in which different players interact pursuing common, different or conflicting objectives. The first purpose of this paper is to discuss the possibility of approaching elementary game theory in high schools. The second objective is to analyze the students’ response in terms of learning, but also of liking. Is it possible “giocare con la teoria dei giochi” (Engl. transl: play with game theory) in the classroom? The third objective is to highlight the possible links between elementary game theory and the grossone-based system introduced by Y.D. Sergeyev. Once again with the didactic aspect of providing high school students with an “easy” and stimulating approach to modern research fields in mathematics. In particular, we describe the approach to a little cycle of lessons of two classes and the performances of a conclusive students’ class test. We will see a great students response, above all regarding the connection between game theory and the grossone system.