Tom Schelling has a famous example illustrating how to solve coordination problems. Suppose you are supposed to meet someone in New York City but you forgot to specify a location to meet. This was before the era of cell phones so there is no opportunity for cooperation before you pick a place to go. Where do you go? You go where your friend thinks you are most likely to go, which is of course where she thinks you think she thinks you are most likely to go, etc.
Notice that convenience or taste or proximity have no direct bearing on your choice. These considerations may indirectly influence your choice, but only if she thinks you think she thinks … that they will influence your choice.
There was an old game show called the Newlywed Game where I learned some of my very early training as a game theorist in my living room roughly at the age of 7. Here is how the show works. 4 pairs of newlyweds were competing. The husbands, say, would be on stage first, with the wives in an isolated room. The husbands would be asked a series of questions about their wives, say “What wedding gift from your family does your wife hate the most?” and the husbands would have to guess what the wives would say. (This was the 70’s so every episode had at least one question about “making whoopee,” like “what movie star would your wife say you best remind her of when you’re makin’ whoopee?”)
When you watch this show every night for as long as I did you soon figure out that the way to win this show is to disregard completely the question and just find something to say that you wife is likely to say, which is of course what she thinks you think she is likely to say, etc. You could try to make a plan with your newlywed spouse beforehand about what to say, something like the first answer is “the crock pot”, the second answer is “burt reynolds” etc. But this looks awkward when the first question turns out to be “What is your wife’s favorite room to make whoopee?” etc.
So the problem is just like Schelling’s meeting problem. The truth is of secondary importance. You want to find the most obvious answer, i.e. the one your wife is most likely to give because she thinks you are most likely to give it, etc. For example, if the question is, “Which Smurf will your wife say best describes your style of makin’ whoopee?” then even though you think the answer is probably “Clumsy Smurf” or “Sloppy Smurf”, you say “Hefty Smurf” because that is the obvious answer.
Ok, all of this is setup to tell you that Gary Becker is clearly a better game theorist than Steve Levitt. Via Freakonomics, Levitt tells the story of a Chicago economics faculty Newlywed game played at their annual skit party. (Northwestern is one of the few top departments that doesn’t have one of these. That sucks.) Becker and Levitt were newlyweds. According to Levitt they did poorly, but it looks like Becker was onto the right strategy, but Levitt was trying to figure out the right answers:
The first question was, “Who is Gary’s favorite economist?” I thought I knew this one for sure. I guessed Milton Friedman. Gary answered Adam Smith. (Although he later apologized to me and said Friedman was the right answer.)
Then they asked, “In Gary’s opinion, how many more quarters will the current recession last?” I guessed he would say three more quarters, but his actual answer was two more quarters.
The next question was, “Who does Gary think will win the next Nobel prize in economics?” This is a hard one, because there are so many reasonable guesses. I figured if Becker writes a blog with Posner, he might think Posner would win the Nobel prize, so that was my answer. Gary said Gene Fama instead.
The last question we got wrong was one that was posed to Gary, asking which of the following three people I would most like to have lunch with: Marilyn Monroe, Napolean, or Karl Marx. I know Gary has a major crush on Marilyn Monroe, so that was the answer I gave, even though the question was about who I would want to have lunch with, not who Gary would want to have lunch with. Gary answered Karl Marx (which makes me wonder what he thinks of me), but did volunteer, as I strongly suspected, that he himself would of course prefer Marilyn to either of the other two.
Cheap Talk 
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May 27, 2009 at 11:52 pm
michael webster
Schelling’s observation was not a version of a nash equilibrium reasoning. There was no implied what do I think that he will think that I think …
Rather, Schelling pointed out that certain features of coordination problems were better solved by figuring out what prominent features existed. Some coordination problems literally solved themselves because they yelled out a solution. Central Station, in the late 50’s, at noon, claimed Schelling, was on such example.
Schelling’s contribution to a realistic theory of strategy was to undermine Nash’s equilibrium reasoning. In Nash’s world, there need not be anybody else. The Nash solution is calculated as if nobody really mattered – it is just the end of the regress of best responses.
But, Schelling’s brilliance was to point out various shortcuts individuals had that made them jump to a non Nash point, as the solution to their coordination problem.
June 3, 2009 at 2:00 pm
kevin quinn
Michael: surely the focal point is a Nash equilibrium, however arrived at? I think I agree with the spirit of what you are saying, if not the letter. Or maybe this is a different point: Schelling says – I don’t have the book here, so this is a paraphrase – that solving a coordination problem essentially requires that “we participate in the creation of a tradition” or something like that. The collective plural is key, the “We.” For the rational players who populate classical game theory, I think he means, the salience or prominence of a particular strategy profile can never be a reason to play one’s part in it: I should play the salient strategy if I believe you will, if I believe you believe I will etc. But the same sort of reasoning can justify playing the non-salient strategy, so we have no positive reason to do either and we are mired in indeterminacy. like Buridan’s ass. The same thing goes for norms or conventions: they can resolve indeterminacy for players who predict the actions of others like they predict the weather, but not for rational players aware of one another’s rationality. The solution for rational players then involves the formation of what the philosopher Margaret Gilbert calls “a plural subject” – which I think is pretty close to Schelling’s “We” who are together to create a tradition. But this kind of blows up methodological individualism. Or as Hegel might say, the problem is “aporetic” for the account of rationality and what it is to act on or for reasons that is employed by game theory and economics generally.
June 5, 2009 at 8:47 am
michael webster
Kevin;
A focal point is indeed stable, but for reasons that are not purely formal. To use the the term “focal point” is to require more information that game theory would ordinarily provide, to find things relevant -say like strategy description- that game theory requires to be irrelevant.
I am not sure I understand your point about salience and reason. I would have thought that the opposite conclusion holds – a salient outcome provides people with reasons to do their part. Perhaps I have misunderstood?
Conventions are ordinarily thought of as relieving individuals of the need to calculate – stopping at a red light, I know longer need to calculate the chances getting through the intersection by jaywalking, if I am following convention – at least Canadian convention. I understand that in New York the convention is different, but equally effective.
I am afraid I have not read Gilbert. My last reading of Hegel was over 20 years ago, so I cannot comment on either of these observations.
December 30, 2010 at 9:02 am
buck
i too remember the NW game. Some answers were in the form of A,B,C.
I remember one couple where the spouses responded before hearing the choices, which resulted in very odd responses. Primitive, but effective.
as for other questions, I agree that disregarding or having chalk responses is the optimal strategy. Chalk responses—room in house, color, present, animal, number(if my memory serves me right “from 1 to 100” (always pick 10), friend(best friend or most disliked–same answer) a couple could win.