Different people have different habits of describing their intents in conversations. Some people may tend to deliberate their full intents in several successive utterances, i.e., they use several consistent messages for readability instead of a long sentence to express their question. This creates a predicament faced by dialogue systems' application, especially in real-world industrial scenarios, in which the dialogue system is unsure that whether it should answer the user's query immediately or wait for users' further supplementary input. Motivated by such interesting quandary, we define a novel task: Wait-or-Answer to better tackle this dilemma faced by dialogue systems. We shed light on a new research topic about how the dialogue system can be more competent to behave in this Wait-or-Answer quandary. Further, we propose a predictive approach dubbed Imagine-then-Arbitrate (ITA) to resolve this Wait-or-Answer task. More specifically, we take advantage of an arbitrator model to help the dialogue system decide to wait or answer. The arbitrator's decision is made with the assistance of two ancillary imaginator models: a wait imaginator and an answer imaginator. The wait imaginator tries to predict what the user would supplement and use its prediction to persuade the arbitrator that the user has some information to add, so the dialogue system should wait. The answer imaginator, nevertheless, struggles to predict the answer of the dialogue system and convince the arbitrator that it's a superior choice to answer the users' query immediately. To our best knowledge, our paper is the first work to explicitly define the Wait-or-Answer task in the dialogue system. Additionally, our proposed ITA approach significantly outperforms the existing models in solving this Wait-or-Answer problem.