Common/mutual knowledge in the laboratory

I talked about mutual knowledge in my open letter to Steve Pinker (blog version HERE, PDF version with additional materials HERE). In the story about the emperor's new clothes, once the emperor stepped outside in his new finery, everyone could see that he was, in fact, naked. The finery was a scam. But it was only when the little boy blurted out "he's naked" that everyone knew that every other person also saw the emperor as naked. That's mutual knowledge.

Now Pinker, a Harvard graduate student, Kyle Thomas, and colleagues at two other schools, Peter DeScioli at Stony Brook University and Omar Haque at Harvard Medical School, have investigated mutual knowledge in the laboratory and reported the results in the Journal of Personality and Social Psychology. Medical Express reports (note: common knowledge = mutual knowledge):

While the notion of common knowledge has existed for decades and has been applied to fields as varied as philosophy and computer science, studies that focused on the actual psychology of common knowledge have been few and far between, Thomas said. 

The chief reason, he said, is that "paying costs to benefit others poses obvious evolutionary puzzles that are not apparent when both people benefit. Because they do not present any evolutionary puzzles, the coordination problems of common knowledge are not nearly as obvious to researchers. The question is, how do we anticipate what our social partners will do, when what they do depends on what they expect us to do? This is a profound social cognition problem. How does one read the mind of a mind reader?"

The had subjects play an economic game where some played the role of a baker and other the role of a butcher. Would they cooperate by producing complementary products (e.g. hot dogs and buns) or would each go his or her own way? It depends on what they knew about one another's activities AND knowledge:

"What we found was that, for private knowledge, even if we varied the payouts, or the number of people involved, only about 15 percent of people cooperated," Thomas said. "With shared knowledge, we saw about 50 percent, and with common knowledge, it was 85 percent. It was just a whopping effect. That indicated to us that we are very sensitive to this previously unappreciated mental state. Our minds evolved to understand this important kind of social structure, and how different kinds of knowledge can impact it."