Very interesting Game Theory article

[bilbo-san]

http://economistsview.typepad.com/ec...xes_of_ra.html

I think Poker and Economics have a lot in common. While reading this article, I was constantly reminded of poker. Specifically, there is a ton of "I know that you know that I know" logic going on.

Just thought everyone might enjoy this.

[AaronBrown]

If you like this kind of thing, look at Beyond Individual Choice by Michael Bachrach. I think he has the right explanation for this kind of behavior.

[KipBond]

In the Traveler's Dilemma (TD), I pick 100. I hope the other person is meta-rational and at least picks 99.

I can't point to exactly why the game theory is wrong here, but I can try to show why this is very different from the Prisoner's Dilemma (PD) (which is what TD becomes if the choices are only "2" or "3").


(image url)

In PD, if I choose "2", I get either "4" or "2". If I choose "3", I get either "3" or "0". Clearly '"4" or "2"' is a better option for me than '"3" or "0"'. This is a true dilemma, because no matter what probability distribution I use for the other person's choice, my choosing '2' still maximizes my EV. Of course, the other person realizes the same thing, so he also picks "2", resulting in both of us getting 1 less than we could have.

The TD is very different. If I assign even a modest probability to the chance that the other person picks a high (90+) number, then I can maximize my EV by also picking a high number. When I consider the fact that there is not a lot of relative difference between "101" and "97" (our results if one of us picks "100" and the other "99"), I might as well pick "100" and hope the other person isn't extremely greedy (to get 1% more by having me get 3% less).

The author himself says he would pick a high number: "probably 95". Why 95? That's irrational. I will pick 100, and you will get 97 instead of the 100 or 101 you could get by picking 100 or 99 respectively.

[fraac]

I ain't much for book learnin', but I knows that when you play against humans, they'll shortcircuit the rationality at predictable points determined by such factors as their inclination to f*ck your sister.

[PantsOnFire]

This didn't make sense to me. I know most of my buddies and myself included would pick 100. We would get 200 from the airline which is the maximum. Picking a lesser number to try and get 4 more than your buddy is ridiculous.

[Gigglegirl]

Well it's a mathematical problem rather than a social/anthropology one.
I think the construct is clumsy though.
If this was applied to real life, answers of 100/100 or perhaps whatever the actual value of the items truly was (50/50?) would hugely predominate IMO.
The reward/penalty is too small to discourage people from trying to gain the max for themselves (100/100) as I see it.

If the person with the lowest quote got $10 more than what they quote and the higher quote got $20 less than the lower quote and the two people involved were going through a vindictive and messy divorce with adultery on both sides........now you're getting into some onemanship hard ball

[AaronBrown]

I wouldn't say the construct is clumsy. The problem is designed to give a mathematical answer (2) that seems absurd. If you made the penalty bigger, the mathematical answer wouldn't seem so odd.

[Gigglegirl]

[ QUOTE ]
I wouldn't say the construct is clumsy. The problem is designed to give a mathematical answer (2) that seems absurd. If you made the penalty bigger, the mathematical answer wouldn't seem so odd.

[/ QUOTE ]

Ok, I can buy that. This is not my field so if I'm completely missing the point here please feel free to correct me.
Why I say the construct is clumsy is because if you are going to invent a scenario, you should make it at least halfway plausible.
I see no reason why people would drop to $2 simply to outdo the opponent when mutual self interest says 100/100 is obvious. What is the incentative to outdo the opponent?
You could use the ever decreasing price total logic to arrive at $2 but as soon as you do, you re-evaluate, follow the same logic and start moving up again due to the fact that both opponents realize they are out playing each other. No?
Also what we haven't considered is the actual price of the goods. If they cost say $50, then $50 is actually the new 'zero'. If both opponents start undercutting each other below the actual value of the goods then they are both losing irrespective of who 'wins'.
Ummm, now I'm confusing myself......
Ok, you're right Aaron, it's just a mathematical problem and I can buy the logic. [img]/images/graemlins/tongue.gif[/img]

[AaronBrown]

You're right that a reasonable person will say $100. A sneak might say $99 and a few people might say $98. But no reasonable person will say less than that, unless they pick the correct price out of honesty, or misunderstand the game.

The problem is it's hard to come up with a mathematical argument for that result, without using ad hoc assumptions or saying people do irrational things. Therefore some people question the value of game theory in general, other people suggest various fixes and get in impassioned arguments about why their fix is natural and everyone else's is silly, and others say the mathematics works and people don't.

I'm in the middle group, except I'm willing to entertain a variety of ideas. I think Bachrach has it right, but I could be wrong.