In multiagent systems autonomous agents interact with each other to achieve individual and collective goals. Typical interactions concern negotiation and agreement on resource exchanges. Modeling and formalizing these agreements pose significant challenges, particularly in capturing the dynamic behaviour of agents, while ensuring that resources are correctly handled. Here, we propose exchange environments as a formal setting where agents specify and obey exchange policies, which are declarative statements about what resources they offer and what they require in return. Furthermore, we introduce a decidable extension of the computational fragment of linear logic as a fundamental tool for representing exchange environments and studying their dynamics in terms of provability.