Event extraction is a fundamental task for natural language processing. Finding the roles of event arguments like event participants is essential for event extraction. However, doing so for real-life event descriptions is challenging because an argument's role often varies in different contexts. While the relationship and interactions between multiple arguments are useful for settling the argument roles, such information is largely ignored by existing approaches. This paper presents a better approach for event extraction by explicitly utilizing the relationships of event arguments. We achieve this through a carefully designed task-oriented dialogue system. To model the argument relation, we employ reinforcement learning and incremental learning to extract multiple arguments via a multi-turned, iterative process. Our approach leverages knowledge of the already extracted arguments of the same sentence to determine the role of arguments that would be difficult to decide individually. It then uses the newly obtained information to improve the decisions of previously extracted arguments. This two-way feedback process allows us to exploit the argument relations to effectively settle argument roles, leading to better sentence understanding and event extraction. Experimental results show that our approach consistently outperforms seven state-of-the-art event extraction methods for the classification of events and argument role and argument identification.