🤖 AI Summary
Common knowledge is foundational for secure group coordination, yet humans frequently conflate finite-order mutual knowledge (e.g., 1st–2nd order) with genuine common knowledge, leading to systematic coordination failures. Method: We introduce the first two-player coordination game paradigm that maps higher-order uncertainty onto ecologically valid scenarios, integrating behavioral experiments (N=802), recursive belief modeling, and formal game-theoretic analysis of coordination structures. Contribution/Results: Participants consistently forced coordination at shallow epistemic depths (1st–2nd order), disregarding substantial penalties—empirically confirming the “mutual knowledge curse”: a cognitive limitation preventing recognition that common knowledge is irreducible to any finite order of mutual knowledge. This demonstrates an intrinsic constraint on recursive reasoning depth that fundamentally limits coordination safety. The findings provide critical cognitive boundary evidence for multi-agent collaboration, institutional design, and AI alignment.
📝 Abstract
Common knowledge is a necessary condition for safe group coordination. When common knowledge can not be obtained, humans routinely use their ability to attribute beliefs and intentions in order to infer what is known. But such shared knowledge attributions are limited in depth and therefore prone to coordination failures, because any finite-order knowledge attribution allows for an even higher order attribution that may change what is known by whom. In three separate experiments we investigate to which degree human participants (N=802) are able to recognize the difference between common knowledge and nth-order shared knowledge. We use a new two-person coordination game with imperfect information that is able to cast the recursive game structure and higher-order uncertainties into a simple, everyday-like setting. Our results show that participants have a very hard time accepting the fact that common knowledge is not reducible to shared knowledge. Instead, participants try to coordinate even at the shallowest depths of shared knowledge and in spite of huge payoff penalties.
