CalBench: Evaluating Coordination-Privacy Trade-offs in Multi-Agent LLMs

Personal AI assistants are beginning to act as delegates with access to calendars, inboxes, and user preferences. Calendar scheduling makes the trust problem concrete: an assistant must coordinate with other assistants while deciding what to reveal about the person it represents. We introduce CalBench, a controlled benchmark for multi-agent calendar scheduling under private information. In each task, N agents manage separate private calendars and schedule a stream of M incoming meetings while minimizing disruption costs. Because no agent can inspect another agent's calendar, success requires language-mediated coordination rather than centralized planning. CalBench generates solvable scenarios with CP-SAT oracle solutions and decentralized non-LLM reference protocols, enabling evaluation of task success, excess cost, communication efficiency, burden fairness, and privacy leakage under matched information constraints. Across seven model families, we find that completion alone misses important failures: agents leave avoidable cost on the table, communication volume does not predict lower regret, and privacy-preserving silence can deprive teammates of cost information needed for fair burden allocation. CalBench provides a reproducible testbed for studying whether autonomous assistants can coordinate on behalf of users before deployment at scale.