In recent years, agents have become capable of communicating seamlessly via natural language and navigating in environments that involve cooperation and competition, a fact that can introduce social dilemmas. Due to the interleaving of cooperation and competition, understanding agents' decision-making in such environments is challenging, and humans can benefit from obtaining explanations. However, such environments and scenarios have rarely been explored in the context of explainable AI. While some explanation methods for cooperative environments can be applied in mixed-motive setups, they do not address inter-agent competition, cheap-talk, or implicit communication by actions. In this work, we design explanation methods to address these issues. Then, we proceed to establish generality and demonstrate the applicability of the methods to three games with vastly different properties. Lastly, we demonstrate the effectiveness and usefulness of the methods for humans in two mixed-motive games. The first is a challenging 7-player game called no-press Diplomacy. The second is a 3-player game inspired by the prisoner's dilemma, featuring communication in natural language.