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This paper experimentally shows that mixed-initiative dialogue is not always more efficient than non-mixed initiative dialogue in route finding tasks. Based on the dialogue model proposed in Conversation Analysis and Discourse Analysis a la the Birmingham school and Whittaker and Stenton's definition of initiative, we implement dialogue systems and obtain experimental results by making the systems interact with each other. Across a variety of instantiations of the dialogue model, the results show that with easy problems, the efficiency of mixed-initiative dialogue is a little better than or equal to that of non-mixed-initiative dialogue, while with difficult problems mixed-initiative dialogue is less efficient than non-mixed- initiative dialogue. [PUBLICATION ABSTRACT]