Detecting groups is becoming of relevant interest as an important step for scene (and especially activity) understanding. Differently from what is commonly assumed in the computer vision community, different types of groups do exist, and among these, standing conversational groups (a.k.a. F-formations) play an important role. An F-formation is a common type of people aggregation occurring when two or more persons sustain a social interaction, such as a chat at a cocktail party. Indeed, detecting and subsequently classifying such an interaction in images or videos is of considerable importance in many applicative contexts, like surveillance, social signal processing, social robotics or activity classification, to name a few. This paper presents a principled method to approach to this problem grounded upon the socio-psychological concept of an F-formation. More specifically, a game-theoretic framework is proposed, aimed at modeling the spatial structure characterizing F-formations. In other words, since F-formations are subject to geometrical configurations on how humans have to be mutually located and oriented, the proposed solution is able to account for these constraints while also statistically modeling the uncertainty associated with the position and orientation of the engaged persons. Moreover, taking advantage of video data, it is also able to integrate temporal information over multiple frames utilizing the recent notions from multi-payoff evolutionary game theory. The experiments have been performed on several benchmark datasets, consistently showing the superiority of the proposed approach over the state of the art, and its robustness under severe noise conditions.