Interesting blogpost on “cognitive hierarchy theory”, which basically seems to involve the empirical examination of how many such steps people use in their actual reasoning when making decisions.
Big surprise: They don’t take it to infinity.
"The cognitive hierarchy theory finds that people only do a few steps of this kind of iterated thinking," [Caltech’s Colin Camerer, Professor of Behavioral Economics] explains. "Usually, it's just one step: I act as if others are unpredictable. But sometimes it's two steps: I act as if others think *I* am unpredictable. You can think of the number of steps a person takes as their strategic IQ. A higher strategic IQ means you are outthinking a lot of other people."
Most of us have a pretty low strategic IQ, but that's to be expected, Camerer notes. To reach a truly high strategic IQ requires either special experience with a particular type of game (such as poker), training, or, in rare cases, special gifts.
Perhaps more interesting to us economists are the implications. The prof says: "We think it means you can fool some of the people some of the time"
That would seem to have “interesting implications” for welfare analysis…. ;-)
On a related note – when I encounter comedy based on this theme I always wonder whether the scriptwriter has studied economics. From the mediocre Ben Stiller comedy “mystery men”:
And the sitcom Friends had this as a central gag to the episode where the friends find out that Monica and Chandler have an affair. You can even get t-shirts with the line “They don't know that we know they know we know.”