November 01, 2004
Cancer between friends
Via Dan Drezner I see that the tiny sack of hand-imported paprika that sits above my sink may be infected with dubious carcinogens.
Still, I figure that since I don't smoke cigarettes I have a certain carcinogen allotment that I might be able to afford to spend on a few grams of spice . . .
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Hand Gestures
Article III Groupie links to a picture of Judge Alex Kozinski imitating a moose. I recently glimped a photo of a very smart HLS conservative also making moose hand gestures. If I see a third digital photo, I may begin to develop a conservative-moose-lawyer conspiracy theory.
Speaking of Article III Groupie, it appears that my classmates are beginning to discover this blog. But I was most amused by a classmate who mentioned this by saying something like, "Will, your blog is pretty cool, but the best thing about it is that it led me to discover Article III Groupie, who is awesome!"
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Bond channels Ibsen
In the latest Bond-Rickey kerfluffle (read the comments), Heidi Bond writes:
[Y]ou don't owe it to me not to be rotten; I don't care if you're rotten or not. But I'm going to guess that you'll like yourself better if you are not rotten than if you are. So maybe you owe it to yourself. And not "owe" in the sense of debt or contract; like in the sense of everyone owing it to themselves to not be a dumbass.
I'm reminded of Dr. Stockmann's line in Henrik Ibsen's best work, An Enemy of the People:
A free man has no right to soil himself with filth; he has no right to behave in a way that would justify his spitting in his own face.
Of course, given that Stockmann devotes most of the play to railing against the evils of democracy, the comparison probably ends there.
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Tipping Points
(Via Marginal Revolution) I see Peter Rossi's discussion of a London restaurant run on a theory of voluntary payment, where you pay what you thought the meal was worth. (If you pay less than the chefs think the meal is worth, though, they refuse your money entirely and thank you very much for trying them out-- clever.)
Given how effective the institution of voluntary tipping seems to be, I'm not surprised that this works. I seem to recall that in The Machinery of Freedom David Friedman proposed running the U.S. national defense off of restaurant tips; that seems a little extreme, but hopefully more restaurants will follow this place's lead.
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The Kick-him-'cause-he's-down equilibrirum
In The Maltese Falcon (mentioned here), when explaining to Mary Astor's character why he is going to turn her in to the fuzz, Sam Spade explains:
If I do this [run off with the falcon] and get away with it you'll have something on me that you can use whenever time you want to. Since I've got something on you, I couldn't be sure that you wouldn't put a hole in me someday.
This reminds me of my most emotionally moving class I ever had at the University of Chicago: Roger Myerson's Game Theory. In Econ 207 he described what I have always called the "kick him while he's down equilibrium":
| Astor trusts | Astor betrays | |
| Spade trusts | 10, 10 | 3, 8 |
| Spade betrays | 8, 3 | 0, 0 |
Game theory mavens, what do you glean from this table? First off, this is no mere prisoner's dilemma. It looks at first like both Mary Astor's character (name unknown) and Sam Spade (Bogary's character) have a perfectly fine equilibrium: If Spade trusts Astor, and Astor trusts Spade, both of them live out their lives in perfect peace without the other bothering them.
Unfortunately, there is more than one equilbirium result to this standoff.
Another possibility is this: Spade decides to betray Astor, taking his surefire minimum payoff of 8, rather than chancing this possibility that she will betray him. Why? Because he is afraid that she, too, will choose to betray him, and he wants to deter her.
[Note that "trust" strictly dominates betrayal. Nonetheless, in a repeated-sum game with the right a priori belief, it can be rational for Spade to betray Astor as he does in the Maltese Falcon. Watch:]
Game theorists interrupt with two possible counter-arguments: 1) Even if Astor chooses to betray him, he will be better off trusting her, and watching things float. 2) Why would Astor betray him? She too will lose...
Witness the magic of game theory. Even though Sam would be better off playing the fall guy for a single round of the Maltese Falcon game, he's even better off if he can somehow credibly commit to a refusal to play the fool. If Astor think he'll never ever trust her, then she has no choice to play into his hands, giving him his guaranteed payoff of 8 every single time.
And why on earth, you ask, would Astor betray him? She surely reads blogs like Crescat and knows that if she betrays Spade she only makes matters worse for both of them. The answer is this: Under the right prior beliefs, Astor betrays Spade because she believes that if she doesn't do so, Spade would betray her. Why would Spade do this? Because he believes that Astor would betray him? Why would she do this? Because she believes that he will betray her? Why would he? Because . . . (ad nauseum).
This is the nauseating "kick-him-while-he's-down" equilibrium, which I respectfully submit might explain a great deal of seemingly self-destructive behavior in two-person high-stakes bargaining games, from film noir to Palestine.
UPDATE:
Let me try to be clearer:
I'm envisioning a simultaneous-move, infinitely-repeated game. What's bizarre about this kind of game is that even though a strategy is completely dominant in a single-play of the game, there can still be other possible equilibria, given the right set of prior expectations.
To generate such an equilibrium, I'll specify a set of expectations for each player, and then we can check to see if those expectations are in equilibrium.
That is, if each player is expected to play the strategy I suggest, will the strategy I suggest be an optimum response on a case-by-case basis? If yes, we have an equilbrium.
So, imagine each player has the following strategy, and thinks that the other player has the following (incomplete) strategy:
1: If the other person played trust and I played betray in the last
round, play "betray" in the next round.
2: If the other person played betray in the last round and I played
trust in the last round, play "trust" in the next round.
3: In other cases, do something, as yet undetermined.
Suppose Astor starts with the move "betray" but Bogart starts with the move "trust", then the first round she gets 8 and he gets 3. What happens next round? Bogart looks at the strategy above, which he thinks Astor is going to adhere to, and concludes that Astor is going to betray him, and therefore decides it's best for him to play "trust" and take his 3.
But will she? If she thinks he's going to play trust, it looks like it's tempting for her to play trust too and deviate from the listed strategy. Then they'll end up at the tempting 10,10 equilbrium. But what then? If Bogart's adhering to the strategy above, then on the next turn he'll play "betray" and take the 8 payoff and stick her with 3. Under a sufficiently low discount rate, that's a very raw deal for Astor.
But would Bogart adhere to the strategy above if Astor played "trust"?
He might if he thought that Astor was going to. And she might if she
thought he was going to. In essence, neither one of them is willing to
risk taking the 10,10 payoff for a turn because they fear that then the
other person will jump first to the 8,3 or 3,8 equilibria from which there
is no escape. So both sides betray only to stop the other side from
betraying them, and the only reason to do that is to stop the other side
from betraying them, and the only reason to do that is . . . .
I'll try to find my notes from Myerson's class and lay this out in much clearer
math . . .
SECOND UPDATE:
Doubters will find the math and the citation to Myerson's book here.
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