The Curse of Shared Knowledge: Recursive Belief Reasoning in a Coordination Game with Imperfect Information

TL;DR

This study explores how humans struggle to differentiate between common knowledge and shared knowledge of various depths in coordination games, often acting as if they have common knowledge despite its absence, leading to potential coordination failures.

Contribution

It demonstrates that humans often mistake shallow shared knowledge for common knowledge in a coordination context, revealing limitations in recursive belief reasoning.

Findings

Humans behave as if they have common knowledge at shallow depths of shared knowledge.

Participants often claim similar certainty levels regardless of actual knowledge depth.

Misinterpretation of shared versus common knowledge can lead to coordination failures.

Abstract

Common knowledge is crucial for safe group coordination. In its absence, humans must rely on shared knowledge, which is inherently 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 involving 802 participants, we investigate the extent to which humans can differentiate between common knowledge and nth-order shared knowledge. We designed a two-person coordination game with imperfect information to simplify the recursive game structure and higher-order uncertainties into a relatable everyday scenario. In this game, coordination for the highest payoff requires a specific fact to be common knowledge between players. However, this fact cannot become common knowledge in the game. The fact can at most be nth-order shared knowledge for some n. Our findings reveal that even at quite shallow depths of shared knowledge (low values of n), players behave as though they possess common knowledge, and claim similar levels of certainty in their actions, despite incurring significant penalties when falsely assuming guaranteed coordination. We term this phenomenon 'the curse of shared knowledge'. It arises either from the players' inability to distinguish between higher-order shared knowledge and common knowledge, or from their implicit assumption that their co-player cannot make this distinction.