You better play 7

mutual versus common knowledge of advice in a weak-link experiment

Giovanna Devetag

Hykel Hosni

Giacomo Sillari

pp. 1351-1381

in: Stephan Hartmann, Chiara Lisciandra, Édouard Machery (eds), Formal epistemology meets experimental philosophy, Synthese 190 (8), 2013.

Abstract

This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental 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 payoff-dominant equilibrium. 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 efficient 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 significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 induces, under suitable conditions, successful coordination more frequently than common knowledge.