In this document, a review of the most important approaches of the Central Places Theory (CPT) postulated by Walter Christaller is carried out. Similarly, an exploration of the different attempts to model this theory in spatial economics is conducted. Furthermore, the paper presents a model based on game theory which is able to pick up certain aspects of the Christaller's CPT such as the hexagonal configuration of the space in which firms compete, as well as the fact that the firms or central places divide the market in equal parts. Also, the behavior of consumers trying to minimize transportation costs and obtain lower prices is studied; this leads them to the closest central places that offer a lower composite price (price + transportation costs). The model shows the existence of a symmetric Nash equilibrium where, despite the fact that a central place is surrounded by 6 firms or central places, the central places compete each other for a specific market area on an isotropic space. Such oligopolistic competition is linked to the hexagonal configuration postulated by Christaller. In other words, the Christaller's hexagonal configuration is coherent with a symmetric Nash equilibrium.