The research field of automated negotiation has a long history of designing agents that can negotiate with other agents. Such negotiation strategies are traditionally based on manual design and heuristics. More recently, reinforcement learning approaches have also been used to train agents to negotiate. However, negotiation problems are diverse, causing observation and action dimensions to change, which cannot be handled by default linear policy networks. Previous work on this topic has circumvented this issue either by fixing the negotiation problem, causing policies to be non-transferable between negotiation problems or by abstracting the observations and actions into fixed-size representations, causing loss of information and expressiveness due to feature design. We developed an end-to-end reinforcement learning method for diverse negotiation problems by representing observations and actions as a graph and applying graph neural networks in the policy. With empirical evaluations, we show that our method is effective and that we can learn to negotiate with other agents on never-before-seen negotiation problems. Our result opens up new opportunities for reinforcement learning in negotiation agents.