Generating appropriate conversation responses requires careful modeling of the utterances and speakers together. Some recent approaches to response generation model both the utterances and the speakers, but these approaches tend to generate responses that are overly tailored to the speakers. To overcome this limitation, we propose a new model with a stochastic variable designed to capture the speaker information and deliver it to the conversational context. An important part of this model is the network of speakers in which each speaker is connected to one or more conversational partner, and this network is then used to model the speakers better. To test whether our model generates more appropriate conversation responses, we build a new conversation corpus containing approximately 27,000 speakers and 770,000 conversations. With this corpus, we run experiments of generating conversational responses and compare our model with other state-of-the-art models. By automatic evaluation metrics and human evaluation, we show that our model outperforms other models in generating appropriate responses. An additional advantage of our model is that it generates better responses for various new user scenarios, for example when one of the speakers is a known user in our corpus but the partner is a new user. For replicability, we make available all our code and data 1 .