The Numbers Game, and Investors as Pornographers

After reading Kevin Hassett’s piece today about politicians treating PE firms as pornographers, I got to perusing Ed Prescott’s 2004 Nobel-acceptance lecture. And that got me thinking about the merits of “rules rather than discretion” in government policies.

As Prescott points out, suppose that nominal wage is set such that real wage is too high. You can, of course, undo this, ex post, via inflation (make people’s money worth less), but if people anticipate that from central banks that will lead to even more inflation and worse distortions. The solution, Nobel-winner Prescott argued, was an independent central bank committed to low inflation.

I’m fond of these sort of exercises, trying to imagine how others will respond to varying policies. There is a great exercise in that sort of thing captured by what is usually called “the numbers game”. Assume that all ten-zillion readers of this blog must choose an integer number between 0 and 100. What will two-thirds of the average number chosen be?


  1. The logical answer is 0, but that assumes all your readers are logical and came up with the same answer. But to assume all your readers are logical is illogical…

  2. 44 is my Derren Brown-ish guess…

  3. 33.
    Average guess is 50. Two thirds of 50 is 33.
    Or is that waaay too simple?

  4. When picking a number between 0 and 100 that’s 2/3 the average, everyone should recognize that they will have to pick something less than 66 (2/3 100). Since everyone knows that, the new max number is 66, so you should pick 2/3 of that (44). Since everyone knows that, you pick 2/3 of that number (30).
    And it keeps going down until you get to 0. This is the “logical” conclusion, but it demands that everyone participating is logical, which is unlikely.

  5. No, not too simple, but the trouble starts with that realization. Once people realize that 33 is the “right” answer, then they’ll assume others will figure that too and act accordingly, so the new “right” answer will be 2/3s of 33 or 22, and then … You get the picture.
    In the limit, the best answer to the above question becomes 0. In the real world, you generally do pretty well with something like 27 or so.