We present a scalable methodology for evaluating language models in multi-turn interactions, using a suite of collaborative games that require effective communication about private information. This enables an interactive scaling analysis, in which a fixed token budget is divided over a variable number of turns. We find that in many cases, language models are unable to use interactive collaboration to improve over the non-interactive baseline scenario in which one agent attempts to summarize its information and the other agent immediately acts -- despite substantial headroom. This suggests that state-of-the-art models still suffer from significant weaknesses in planning and executing multi-turn collaborative conversations. We analyze the linguistic features of these dialogues, assessing the roles of sycophancy, information density, and discourse coherence. While there is no single linguistic explanation for the collaborative weaknesses of contemporary language models, we note that humans achieve comparable task success at superior token efficiency by producing dialogues that are more coherent than those produced by most language models. The proactive management of private information is a defining feature of real-world communication, and we hope that MT-PingEval will drive further work towards improving this capability.