In this paper, we study the problem of addressee and response selection in multi-party conversations. Understanding multi-party conversations is challenging because of complex speaker interactions: multiple speakers exchange messages with each other, playing different roles (sender, addressee, observer), and these roles vary across turns. To tackle this challenge, we propose the Speaker Interaction Recurrent Neural Network (SI-RNN). Whereas the previous state-of-the-art system updated speaker embeddings only for the sender, SI-RNN uses a novel dialog encoder to update speaker embeddings in a role-sensitive way. Additionally, unlike the previous work that selected the addressee and response separately, SI-RNN selects them jointly by viewing the task as a sequence prediction problem. Experimental results show that SI-RNN significantly improves the accuracy of addressee and response selection, particularly in complex conversations with many speakers and responses to distant messages many turns in the past.