Multiagent research provides an extensive literature on formal Beliefs-Desires-Intentions (BDI) based models describing the notion of teamwork and cooperation. However, multiagent environments are often not cooperative nor collaborative; in many cases, agents have conflicting interests, leading to adversarial interactions. This form of interaction has not yet been formally defined in terms of the agents mental states, beliefs, desires and intentions. This paper presents the Adversarial Activity model, a formal Beliefs-Desires-Intentions (BDI) based model for bounded rational agents operating in a zero-sum environment. In complex environments, attempts to use classical utility-based search methods with bounded rational agents can raise a variety of difficulties (e.g. implicitly modeling the opponent as an omniscient utility maximizer, rather than leveraging a more nuanced, explicit opponent model). We define the Adversarial Activity by describing the mental states of an agent situated in such environment. We then present behavioral axioms that are intended to serve as design principles for building such adversarial agents. We illustrate the advantages of using the model as an architectural guideline by building agents for two adversarial environments: the Connect Four game and the Risk strategic board game. In addition, we explore the application of our approach by analyzing log files of completed Connect Four games, and gain additional insights on the axioms' appropriateness.