Strategic Uncertainty

• Theory of Mind

Nature is not the only source of risk. In strategic situations, the fact that players have influence on the outcomes of opponents often leads to another type of uncertainty, strategic uncertainty. This can be seen even in the simplest of games, such as matching pennies. There, one player, the matcher, is paid if his move is the same as that of the opponent. The other player, the mismatcher, is rewarded only if her move is different from that of the opponent. Optimal play requires that players correctly guess the upcoming move of the opponent. This means that players must "put themselves in the mind of the opponent." This is what psychologists refer to as "theory of mind" (some autistm and schizophrenia patients are particularly bad at this). Mathematicians called game theorists claim that eventually this will lead to play where you don't have to think about the opponent - you just have to try to be random in a way that the opponent is indifferent in choosing his move. (This is the celebrated "Nash equilibrium.)

Our research has shown, however, that humans constantly try to outsmart the opponent; they think "theory of mind" throughout. This property of human behavior has allowed us to elucidate the computations taking place in the "social" parts of the cortex (medial prefrontal cortex and junction of the temporal and parietal parts of the cortex). There, neural signals reflect prediction of what the opponent will do given one's own moves.

We have also compared this to how non-human primates such as chimpanzees play this game. Surprisingly, chimpanzees do play Nash! This is particularly amazing because chimpanzees need to learn the incentives (payoffs) of the opponent through play of the opponent and hence, unlike mathematicians, can't really "think through" the Nash equilibrium. They learn to play Nash by experience... When we asked humans to play matching pennies without knowing what the payoffs of the opponent were, the best they could do is to just flip a coin!

Humans seem often to think that large-scale social institutions such as financial markets have a "mind of their own." We showed how this actually helps them perform better when there are others in the market with better information. On the other hand, theory of mind is detrimental when there are bubbles... In that case, we found that the social parts of the brain incorrectly track the order arrival process to detect insiders even when everyone knows there are no insiders. Maybe the bubble itself makes them believe that someone out there is smarter than they are?