On Wed, Jul 17, 2002 at 06:49:04PM -0700, Hal Finney wrote:
> OK, I understand now that the utilities below are the utilities for A
> and B when S gets the various items.  So U(TV) is the utility for A for
> S to get a TV, which is the same as the utility for B since they are
> identical copies.

Yes.

> > According to my incorrect analysis, SSA would imply that you choose option 
> > 2, because that gives you .5*U(TV2) + .5*U(TV) > .5*U(TV) + .5*U(stereo) 
> > since U(TV2) > U(stereo). I argued that you should consider yourself A and 
> > B simultaneously so you could rationally choose option 2, because 
                                                           ^
I meant "option 1" here -----------------------------------^

> > U({TV,stereo}) > U({TV2, TV}).
> 
> Yes, that makes sense.
> 
> > However taking both SSA and game theory 
> > into account implies that option 2 is rational. Furthermore, my earlier 
                                     ^--- this should be "1" as well
> > suggestion leads to unintuitive results in general, when the two players 
> > do not share the same utility function.
> 
> I know you meant to write that game theory implies that option 2 is
> irrational.

Yes. I meant to write "option 1" in two places where I actually 
wrote "option 2". Sorry!

> If option 2 is also a Nash equilibrium, that is better than option 1,
> right?  

No, option 1 is better than option 2, because S prefers a TV and a stereo 
to two TVs.

> This is why option 2 was preferred under the first analysis.
> However I see that under this reasoning there are utility assignments
> which make option 1 be a Nash equilibrium while option 2 is not, hence
> option 1 would be preferred in those cases, despite the earlier reasoning
> which would choose option 2.

No, I think you got confused because of my typos.

I'll answer the rest of your post later. I want to resolve this 
misunderstanding ASAP.

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