North Western Winds

Contemplating it all from the great Pacific Northwest

The Traveler’s Dilemma

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This quote is taken from a Scientific American story on game theory problem called The Traveler’s Dilemma:

Suppose you and I are two smart, ruthless players. What might go through our minds? I expect you to play a large number–say, one in the range from 90 to 99. Then I should not play 99, because whichever of those numbers you play, my choosing 98 would be as good or better for me. But if you are working from the same knowledge of ruthless human behavior as I am and following the same logic, you will also scratch 99 as a choice–and by the kind of reasoning that would have made Lucy and Pete choose 2, we quickly eliminate every number from 90 to 99. So it is not possible to make the set of “large numbers that ruthless people might logically choose a well-defined one, and we have entered the philosophically hard terrain of trying to apply reason to inherently ill-defined premises.

If I were to play this game, I would say to myself: “Forget game-theoretic logic. I will play a large number (perhaps 95), and I know my opponent will play something similar and both of us will ignore the rational argument that the next smaller number would be better than whatever number we choose. What is interesting is that this rejection of formal rationality and logic has a kind of meta-rationality attached to it. If both players follow this meta-rational course, both will do well. The idea of behavior generated by rationally rejecting rational behavior is a hard one to formalize. But in it lies the step that will have to be taken in the future to solve the paradoxes of rationality that plague game theory and are codified in Traveler’s Dilemma.

Of course that doesn’t make a lot of sense without reading the article, where the game is explained, so I’d do that.

Like the Prisoner’s Dilemma, on which it is modelled, this game gives a fascinating insight into how what we might call “rationalist minimalism” can lead us astray. What puzzled me was the assumption that my “best response” has to be one that leads me to a better result than my opponent. That drives the “Nash equilibrium” to $2, which can clearly be bettered if the two players don’t get too torn up over which one of them gets the largest amount. It’s a bit like a “one in the hand beats two in the bush” scenario. If we both see this, then going for the larger number is not so hard to see. It costs me nothing if my opponent gets a large sum too.

Also from the article:

The game and our intuitive prediction of its outcome also contradict economists’ ideas. Early economics was firmly tethered to the libertarian presumption that individuals should be left to their own devices because their selfish choices will result in the economy running efficiently. The rise of game-theoretic methods has already done much to cut economics free from this assumption. Yet those methods have long been based on the axiom that people will make selfish rational choices that game theory can predict. TD undermines both the libertarian idea that unrestrained selfishness is good for the economy and the game-theoretic tenet that people will be selfish and rational.

It also brings into question an atomist understanding of how societies work, with each of us being lone rangers making choices based on our own thinking through of any problem that comes our way. When do act on such ideas, problems arise. If the subject interests you, EF Schumacher and/or commentaries might interest you.

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Written by Curt

May 22, 2007 at 6:00 pm

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