I'd like to mention two kinds of less common teaching environments: the role-playing or alternate reality simulation, and the hackathon. They both have aspects of co-learning, and they both set radical time limits on the learning curve, but they have somewhat different takes on the authority angle.
With the RPG / ARG simulation, you literally have Plato's allegorical cave. In this scenario, there is a "game master" or other named ultimate authority whose job it is to completely describe all aspects of the simulated world outside of the participant's perception. The job of the student / participant is to rapidly learn everything they need to know about their motivations and role in the world and then work with the authority and the other students to achieve their personal goals and possibly other group goals within that world.
We achieved this to great effect at Worcester Polytechnic Institute 20 years ago when we ran a simulation of collaboration between world space agencies to explore cooperation and competition between different organizational mindsets with conflicting goals and various motivations. Participants needed to absorb huge amounts of information in very short time - learning about the agencies, their personal histories, agency histories, past interactions with their agency and others, with other individuals... it's a massive task, but one well suited to a social animal! And the information retention is also excellent post-simulation as a result of that heavily social interaction.
(It goes without saying that this kind of model can be adapted easily to historical recreations / simulations of all kinds to gain greater empathy and understanding of historical events)
On the other hand, we have the hackathon, a fairly recent form of collaborative learning environment enabled by rapid prototyping technologies and advances in computer technology. Cross-functional interdisciplinary teams, often of strangers, organically form around common interests and work together in a high pressure, strictly time limited situation - a "hacking marathon" (where "hacking" is understood to be cobbling together a solution of some kind, not breaking into a secure system).
The only sort of authority one usually finds in these mass collaborations/competitions to solve specific problems is "judging" which happens at the end of an event, and is very much an afterthought of the learning process. You can have mentors or coaches who can give advice or otherwise provide guidance or expertise to a team, but even that authority is very much an option and not a requirement. Participants have to learn from each other and mentor one another very quickly - sometimes cramming to learn entirely new technologies or skillsets in hours or in a day.
Problem solving is a key element in both of these learning environments. And even though authority is omnipresent in the RPG/ARG scenario, it isn't completely essential either; a great "game master" is one who lets the participants drive the events and then improvises new results and conditions in the simulated world instead of "railroading" them to a common conclusion every time the simulation is run.
Thanks for reading! Would love to chat further.