Short answer
The useful part first.
Pax Autocratica is single-player in the current Early Access build. The Steam page says co-op is a major feature the team hopes to develop during Early Access, but it gives no release date and does not guarantee that feature.
What is playable now?
The official Steam feature list shows Single-player, Steam Cloud, and Family Sharing. It does not list online co-op, LAN co-op, or multiplayer. Buy the current build only if its single-player experience is enough for you today.
What did the developer say about co-op?
In the Early Access description, Multiverse calls co-op one of the major features it hopes to develop during Early Access. “Hope to develop” is directional language—not a roadmap date, finished feature, or guarantee that every planned mode will ship.
How long could that take?
The same store page estimates roughly two years in Early Access, while warning that the schedule can change with feedback and development. There is no official co-op launch window at this check.
What should co-op buyers do?
Follow the official Steam news feed and verify that the store feature list actually includes co-op before purchasing for a group. Do not rely on search snippets, wish lists, or the presence of “co-op” in a future-feature discussion.