Detecting and preventing the adversarial action of an agent with respect to the community of agents can be a serious issue in the design of open multi-agent systems. This task is severely domain dependent and it is hard to find a general solution. This contribution presents a utility based model of adversarial action and analyses few properties of adversarial behavior in multi-agent systems. Potential use and important drawbacks of this model are discussed in the paper. Categories and Subject Descriptors I.2.11 [Distributed Artificial Intelligence]: Multiagent systems General Terms Theory Keywords Adversarial action, Cooperation, Competitiveness, Formal model