You better play 7: Mutual versus common knowledge of advice in a weak-link experiment

This paper presents the results of an experiment on mutual versus common knowl- edge of advice in a two-player weak-link game with random matching. Our experimen- tal subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payo-dominant equilib- rium. In the mutual knowledge of level 1 treatment, the suggestion appears on every subject's monitor at the beginning of every round, with no common knowledge that everybody sees the same suggestion. In the mutual knowledge of level 2 treatment, the same suggestion appears on each subject's monitor, accompanied by the request to send the suggestion to the partner in the round, followed by a notication that the message has been read. Finally, in the common knowledge treatment, the suggestion is read aloud by the experimenter at the end of the learning phase. Our results are somewhat surprising and can be summarized as follows: in all our treatments both the choice of the efficiency-inducing action and the percentage of e cient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to signicantly increase the salience of the e cient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 (as the one occurring in our message treatment) induces successful coordination more frequently than common knowledge.