  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.
