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Taking a Hint or Coordinating Expectations

We have been exploring the conflict between Stick/Frank and Sportree/Leon after the bank robbery went bad.

I used some simple game theory vocabulary. We translated the dialogues between the protagonists and deduced that they had the following preference structures.

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:

For many, even those readers with formal training, the translation exercise is both difficult and apparently pointless. (I find translating dialogues into preference models hard and usually make mistakes; I have 35 years of experience doing this!)

So, even simple models are hard. What makes this modeling useful?

A good argument can be made that all the real work, the strategic inferences took place in the dialogues that the formal model was a mere artifacts which added nothing.

However, this would be a mistake. It is far from clear that this conflict has the preference structure we deduced: an outcome which is best for both parties, that they cannot get to.

We also now have a general structure. In Swag, the end result is that the parties coordinate their expectations in a way such that all parties wind up badly. Stick/Frank are jailed for the murder of Sportree/Leon - the latter no doubt having legitimately higher expectations than being Stick's 3rd and 4th murder victim.

Stick and Sportree coordinated their expectations around the realization that

"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."

But only Stick knew that they had so coordinated, and knew that Sportree didn't know what Stick knew.

"One advantage, he doesn't know what we know [that we were set-up] And he must think that we are pretty dumb to begin with."

Now the value of our formal model is not that it provides us with a calculation or reason for Stick to plan for Sportree's ambush. In some sense, we had to know that in order to model the conflict.

The real value of the mode is that we now have two general preference structures, a description of beliefs, and expectations that can use to identify other conflicts as structurally the same as this one. We can gain some insight into the general problem of why the trusted go between, in this case Frank, fails to change the dilemma game into a situation in which the optimal point is focal.

The model makes it crystal clear that Stick/Frank and Sportree/Leon are in a damned odd type of conflict: each agrees that O2 is the unique best solution, but they end up in jail or dead because what we have here is a failure to communicate.

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Full post as published by Misleading Advertising Law on July 08, 2008 (boomark / email).