How to Cheat Your Partners and Make it Stick
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Stephen Dubner asked what one question would you ask one of three hypothetical partners, if you were going to select them to play a one shot prisoner's dilemma game.
Pretty interesting idea.
Some of the answers were interesting, but the problem was too unconstrained. It would have been better to ask: given that you want the other person to do X, what one question would you ask that would provide good evidence that the person would do X?
Obviously, if you expect the person to play the dominant strategy, virtually any question will do.
But if you want the other person to depart from the "norms of economic rationality", you have a more interesting problem.
In the previous post, I discussed how the noted crime novelist, Elmore Leonard, dealt with a variant of the prisoner's dilemma problem.
To summarize, Stick and Frank were two stick-up gangsters that were engaged by Sportree and Leon to hold-up a department store.
Things went wrong: Frank saw Leon kill in cold blood one of their gang, and Stick was arrested by the Detroit police when he tried to pick up the loot that the gang stashed in department store.
Sportree and Leon planned to kill Stick and Frank, while pretending to take them to pick up the money. But, Stick somehow figured out the plan, smuggled in a gun - despite being expertly searched by Leon- and killed both Sportree and Leon.
How did Stick figure out Sportree's strategic choice, and plan accordingly?
This is a very interesting question in strategic reasoning, which needs a few abstract models to clarify the reasoning as distinct from rational calculation.
Consider the matter from Stick's viewpoint.
Call the choice on the left, "L" and the choice on the right "R".
There is much to be said for either choice. Indeed, Stick's intended choice is "L". He has already been in jail, but he believes that he can beat this rap.
But Leon has already doubted Stick's ability to commit to L, observing that "it'd be nice he don't say nothing. And they say to him, "Thank-you, we sorry we bother you, man, let him go. That'd be nice." Yeah, it would be nice - doesn't sound like Leon thinks "it be happening."
Sportree's decision viewpoint is this:
Again, for the sake of abstraction, call the choice on the left, "L" and the choice on the right "R".
Here is the strategic overview, which for technical reasons is not a game, let alone a normal game.
Now how do each of Sportree and Stick evaluate this strategic decision?
We have been told that Stick would prefer most not to make a deal with the police.
Let's work back through the abstractions.
O1 is {L,L} which is Stick keeps quiet, but Sportree tries kill him anyways.
O2 is {L,R} which is Stick keeps quiet, and Sportree lets Frank and him walk.
O3 is {R,L} which is Stick does a deal, and Sportree tries to kill him.
O4 is {R, R} which is Sticks does a deal, and Sportree lets Frank and him walk, anyways.
Let ">" stand for "Stick or Sportree prefers". For, Stick this is his preference relation.
O2 is clearly Stick's most preferred outcome. Overall, he would prefer to have Sportree let him walk. If, Sticks does a deal, then obviously he would prefer that Stick lets him and Frank walk. Finally, his worst outcome is to have Stick try to kill him, while he has committed to not cooperating with the police.
For Sportree, this is his preference relation:
If Sportree could trust Stick to be "friends' there would be no point in trying to kill him. But, if Sportree is going to try to kill Stick, it would be better to do it before Stick decides to do a deal with the police. Finally, it would be terrible for Sportee if Stick did the deal and Sportree had resolved to let him walk.
Now, here is the very odd part of this game. O2 is both parties best outcome, dominating all other outcomes.
But, as Elmore Leonard writes it, the characters end up at O1. Stick can beat the rap, but Sportree is going to try to kill both Stick and Frank.
And it is an entirely believable plot.
There are no dominant strategies - so why do the characters miss out on the optimal solution, which is also a Nash equilibrium point?
In the next entry, we will examine the strategic thinking that prevents these two characters coming to the the optimal solution, produce a training exercise to reproduce this problem, and illuminate some of the other strategic problems Leonard writes about.
But here is a hint from Stick:
"But, Sportree, Leon, they're not going to hold their smoke waiting to see what I do. Leon shot Billy Reiz, you were standing there."
