Tuesday, August 02, 2005

Don't Get Screwed

Everyone knows how you divide a pie equally between two people, right? One person does the dividing, the other picks which half they want. In the standard game theory formulation, there is a Nash equilibrium when the divider splits the pie exactly in half and the picker picks whichever half they feel like, since they are the same.

So which would you rather be? Obviously, it doesn't matter because everyone gets exactly half either way. But what if you aren't very good at dividing the pie? What if there's some random error? Then it's definitely best to be the picker. If there's any chance at all the the cut won't be exactly 50-50 then the expected value of the *larger* slice is greater than the expected value of the smaller slice.

So don't get screwed, always try to be the picker.

2 Comments:

Blogger Isaac said...

Less likely, but you might also have problems in perception between the two already cut pieces (when two pieces of cake are almost the same size, can you tell which is larger? Perhaps easier just to choose the middle of the pie). This perception problem may well be the root cause of random error in cutting. While choosing seems easier than cutting, it is possible that the error could come at either side. So I'm not sure it is so clear cut that you want to be the picker.

11:25 PM  
Blogger henry said...

Excellent point. But if you never perceive the real difference than what does it matter if you pick the truly smaller piece? You still get what you want.

On the other hand, if you suppose players learn the true size of pieces after the cutting and picking is over then things get more complicated.

7:18 AM  

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