Ch. 1: Iterated dominance

[Aaron Swartz]

I'm confused by the top of p. 35, which says that games that don't
have a Nash equilibrium might get one if you start eliminating
strictly dominated options from other players' strategy sets:

> _iterated dominance_ is a procedure by which a player may eliminate from consideration any of the _other_ players’ strategies that are
strictly dominated (i.e., would not be advantageous to adopt in any
strategy profile). Truncating the other players’ strategy sets in this
manner changes the structure of the game such that the game truncated
by iterated dominance may have a Nash or dominant strategy equilibrium
even though the complete game did not.

My reasoning runs as follows:

a) in a Nash equilibrium no one can unilaterally switch to a better strategy
b) iterated dominance removes strictly dominated options
c) by definition, strictly dominated options are always dominated by a
better strategy
d) thus they would never be considered or used in a Nash equilibrium
e) thus removing them couldn't possibly affect a Nash equilibrium

Where did I go wrong?

[Chris Mealy]

I'm doing a little remedial reading on game theory. I'll let you know
if I figure it out.

[Chris Mealy]

Thanks to youtube I think I get this now. The problem starts with
"games that _don't_ have a Nash equilibrium ..." But in your lettered
reasoning you're assuming you do have a NE. Here's a good example. It
starts off with no dominating strategies, but through successively
removing dominated strategies you get to the NE.

http://www.youtube.com/watch?v=NoMfCQlVC0A#t=44m11s

I'm glad you brought this up. I hadn't realized this had gone over my
head, and I wouldn't have taken the time to track it down otherwise.

On Aug 23, 2009, at 7:19 AM, Aaron Swartz wrote: