[ExI] nash equilibrium again

[Anders Sandberg]

spike <spike66 at att.net> , 17/2/2014 5:05 PM:


 

 Scenario: the pirate ship is spotted by the navy, battle ensues, cannonball thru the pirate ship’s hull, blub blub blub, ...

...As she fades in the distance, she hears a shot.  This too is perfectly logical: the remaining two pirates are not in a Nash equilibrium, not even a metastable one that existed temporarily with the three of them.  She quickens her pace, since there is now one living pirate with a few coins.  She and that guy aren’t in a Nash equilibrium either.  She isn’t motivated to risk her many coins for a few more, but he is motivated to risk his few for her many.

 

OK now could we argue that the three pirates were never in a Nash equilibrium to start with?

Hehehe... this pirate problem has a surprising depth. It gets even more awesome when you start considering larger groups. In many ways a worthy successor of Mrs Santa's north and east run.
Now, the definition of Nash equilibria is that knowing the other players' strategies they still do not change their strategy. So in each of the subgames things are all right as long as they only plan for surviving that game. But since one could also see them as steps along the way to an end-game. So the key thing is would players change strategies based on this? It seems that there would be larger equilibria here too.


Anders Sandberg, Future of Humanity Institute Philosophy Faculty of Oxford University
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