The design of agents interacting with human beings is becoming a crucial problem in many real-life applications. Different methods have been proposed in the research areas of human-computer interaction (HCI) and multi-agent systems (MAS) to model teams of participants (agents and humans). It is then necessary to build models analyzing their decisions when interacting, while taking into account the specificities of these interactions. This paper, therefore, aimed to propose an explicit model of such interactions based on game theory, taking into account, not only environmental characteristics (e.g., criticality), but also human characteristics (e.g., workload and experience level) for the intervention (or not) of agents, to help the latter. Game theory is a well-known approach to studying such social interactions between different participants. Existing works on the construction of game matrices required different ad hoc descriptors, depending on the application studied. Moreover, they generally focused on the interactions between agents, without considering human beings in the analysis. We show that these descriptors can be classified into two categories, related to their effect on the interactions. The set of descriptors to use is thus based on an explicit combination of all interactions between agents and humans (a weighted sum of 2-player matrices). We propose a general model for the construction of game matrices based on any number of participants and descriptors. It is then possible to determine using Nash equilibria whether agents decide (or not) to intervene during the tasks concerned. The model is also evaluated through the determination of the gains obtained by the different participants. Finally, we illustrate and validate the proposed model using a typical scenario (involving two agents and two humans), while describing the corresponding equilibria.