Comment on Nash Equilibria and Schelling Points

Sun, 01 Jul 2012 09:32:44 GMT

How do you determine the value for having a particular resistance to blackmail, such that you can distinguish between blackmail you should and shouldn't give in to?

The doctor has no obvious reason to prefer you to want to save your wife or your child. On the other hand, the mugger would very much prefer you to hand him your wallet than to accept to be killed, and so he's deliberately making the latter possibility as unpleasant to you as possible to make you choose the former; but if you had precommitted to not choosing the former (e.g. by leaving your wallet at home) and he had known it, he wouldn't have approached you in the first place.

IOW this is the decision tree:

         mug                   give in
 ------------------------------------------------ (+50,-50)
   |                       |
   |                       |   don't give in
   |                       ---------------------- (-1,-1e6)
   |  don't mug
   ---------------------------------------------- (0, 0)

where the mugger makes the first choice, you make the second choices, and the numbers in parentheses are the pay-offs for the mugger and for you respectively. If you precommit not to choose the top branch, the mugger will take the bottom branch. (How do I stop multiple spaces from being collapsed into one?

Discuss