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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>A few months ago we got talking about Nash equilibrium here. Anders was up to speed on it, so I am hoping he or one of the other math/philosophy hipsters will be able to untangle this.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Scenario: the pirate ship is spotted by the navy, battle ensues, cannonball thru the pirate ship’s hull, blub blub blub, navy is hanging the survivors from yard arms, but three pirates manage to escape in a lifeboat. They row like crazy in the moonless night. When morning comes, it appears fortune is with them, for they discover the navy ship is nowhere to be seen, the lifeboat has drifted ashore near a town, and that the captain hid the loot in the lifeboat! Along with three loaded guns! Each take one gun, the kind they had in the old days, a huge lead ball driven by an absurd amount of powder, so if one gets shot with one of those, they are ruined, game over man, arrrr…<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>They sit on the beach and start to divide the gold doubloons in the usual way, dealer starts the old one for you, one for you, one for me, repeat a number of times, but the dealer was a logic professor before she gave it up for the piracy business. She knows about Nash equilibria. The next round goes one for you, one for you, two for me… Both the other pirates turn their weapons on her, but she knows neither will fire, for as soon as either one does, that guy is unarmed with one dead pirate (the dealer) one armed pirate and a sack of gold coins. The outcome of that doesn’t require a math degree to predict. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>She is right of course, both aim their weapons, neither fires. So she continues, one for you, one for you, three for me, and the next time, five for me, and keeps Fibonnacci-ing for a few rounds, but then abruptly stands up with the remaining gold, and bids them good day. She walks away with most of the gold, knowing neither will shoot, for the same reason as before: he who shoots, dies by the other. Nothing personal, it’s just business, it’s what pirates do, along with saying arrrr much too often.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>OK now could we argue that the three pirates were never in a Nash equilibrium to start with?<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>spike<o:p></o:p></p></div></body></html>