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

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.