# [FoRK] The Traveler's Dilemma

Jeff Bone <jbone at place.org> on Thu May 24 07:30:57 PDT 2007

```On May 23, 2007, at 6:36 PM, Russell Turpin wrote:

> The logic does assume each player is trying to maximize his own
> payout.
> The problem is more that it assumes a series of maximizing steps must
> present the maximal solution. Thus, \$99 is a better play than \$100,
> and
> likely is in reality, since most people will write down a \$100, and
> your payoff thus is \$101. But then begins the recursion down to \$2.
> And
> that doesn't work. In this regard, this hole in game theory seems
> related to the paradox of the unexpected hanging:
>
> http://en.wikipedia.org/wiki/Unexpected_hanging_paradox

Indeed.

The presentation of the problem is weak, but the Nash analysis is
textbook (given a correct presentation.)

Interesting variations:  consider the case of iterated TD, for an
uncertain number of iterations, against a single opponent of any
strategy.  What's the optimal strategy?  Now generalize:  iterated TD
tournament, unknown number of players, uncertain number of iterations
per player.

Tit-for-tat (and friends, i.e. two-tits-for-a-tat --- hey, that
sounds like a stripper thing! ;-) rears its ugly head again...

jb

```

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