In this paper, we discuss the advantages of investigating primate societies to build Multi-Agent Systems, and we present our preliminary results in this context. We first give an overview of primates' social competences, then we draw a parallel between the main problems found in the study of primate societies (regarding their social organization) and some of the most commonly encountered issues when designing Multi-Agent Systems. We describe a model of social cognition and perception that we have experimented. Its results show that some social concepts can be implemented by attaching importance to the interactions between the agents, instead of using a complicated individual-based model. Finally, we discuss the main extensions we are working on and propose applications to Multi-Agent technology.