Reigns of Error


Rajiv Sethi over at his website:

The death of Kenneth Arrow has led lots of people to swap stories about their interactions with him. Larry Blume has posted several of these on facebook, including the following response to my own contribution (quoted with permission):

This story is not at all surprising; Ken read everything. I think I mentioned elsewhere that my last conversation with Ken, this past June, concerned The Theory of Moral Sentiments. He and Amartya Sen were taking turns quoting from it, from memory… I could recognize the quotes, but not respond in kind. Once in a conversation about Nash equilibrium and rational expectations, Ken wondered if I had read Merton on expectations – not Robert Jr.: He also had a good stock of Shakespeare to call on.

The link is to a 1948 paper by the great sociologist Robert K. Merton (father of the Nobel-winning economist). Reading anything at all by Merton is an excellent use of one's time, so I went through this paper. It's extraordinary. Not only does Merton provide a very clear account of equilibrium beliefs, but goes on to point out that even when these beliefs are correct in a narrow sense, they can hold in place an incorrect understanding of the social world. To translate this into the contemporary language of economics, Merton points out that the play of equilibrium strategies can go hand in hand with a deeply erroneous understanding of the game.
Merton begins with an account of a Depression-era bank run that perfectly captures the multiple equilibrium logic he has in mind:

It is the year 1932. The Last National Bank is a flourishing institution. A large part of its resources is liquid without being watered. Cartwright Millingville has ample reason to be proud of the banking institution over which he presides. Until Black Wednesday. As he enters his bank, he notices that business is unusually brisk. A little odd, that, since the men at the A.M.O.K. steel plant and the K.O.M.A. mattress factory are not usually paid until Saturday. Yet here are two dozen men, obviously from the factories, queued up in front of the tellers' cages. As he turns into his private office, the president muses rather compassionately: "Hope they haven't been laid off in midweek. They should be in the shop at this hour."

But speculations of this sort have never made for a thriving bank, and Millingville turns to the pile of documents upon his desk. His precise signature is affixed to fewer than a score of papers when he is disturbed by the absence of something familiar and the intrusion of something alien. The low discreet hum of bank business has given way to a strange and annoying stridency of many voices. A situation has been defined as real. And that is the beginning of what ends as Black Wednesday — the last Wednesday, it might be noted, of the Last National Bank.

You can see why Arrow saw in this a precursor to the concept of Nash equilibrium, the existence of which would be established just two years later.
More here.