Comment on Nash Equilibria and Schelling Points

Fri, 29 Jun 2012 14:55:31 GMT

...because it's very hot in Pirate Island's shark-infested Pirate Bay, not out of any fear or distress at an outcome that put her in a better position than she had occupied before.

Whereas A had to build an outright majority to get his plan approved, B just had to convince one other pirate. D was the natural choice, both from a strict logico-mathematical view, and because D had just watched C and E team up to throw their former captain overboard. It wasn't that they were against betraying their superiors for a slice of the treasure, it was that the slice wasn't big enough! D wasn't very bright--B knew from sharing a schooner with him these last few months--but team CE had been so obliging as to slice a big branch off D's decision tree. What was left was a stump. D could take her offer of 1 coin, or be left to the mercy of the outrageously blood-thirsty team CE.

C and E watched on, dreaming of all the wonderful things they could do with their 0 coins.

[I think the "rationality = winning" story holds here (in the case where A's proposal passes, not in this weird counterfactual cul-de-sac) but in a more subtle way. The 98 0 1 0 1 solution basically gives a value of the ranks, i.e., how much a pirate should be willing to pay to get into that rank at the time treasure will be divided. From this perspective, being A is highly valuable, and A should have been willing to pay, say, 43 coins for his ship, 2 coins for powder, 7 coins for wages to B, C, D, E, etc., to make it into that position. C, on the other hand, might turn down a promotion to second-in-command over B, unless it's paired with a wage hike of one 1 coin; B would be surprisingly happy to be given such a demotion, if her pay remained unchanged. All the pirates can win even in a 98 0 1 0 1 solution, if they knew such a treasure would be found and planned accordingly.]

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