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  "events": [ {
    "tStartMs": 7204,
    "dDurationMs": 4459,
    "segs": [ {
      "utf8": "Two perfectly rational gingerbread men,\nCrispy and Chewy,"
    } ]
  }, {
    "tStartMs": 11663,
    "dDurationMs": 3375,
    "segs": [ {
      "utf8": "are out strolling \nwhen they’re caught by a fox."
    } ]
  }, {
    "tStartMs": 15038,
    "dDurationMs": 2583,
    "segs": [ {
      "utf8": "Seeing how happy they are, \nhe decides that,"
    } ]
  }, {
    "tStartMs": 17621,
    "dDurationMs": 2000,
    "segs": [ {
      "utf8": "instead of simply eating them,"
    } ]
  }, {
    "tStartMs": 19621,
    "dDurationMs": 4083,
    "segs": [ {
      "utf8": "he’ll put their friendship \nto the test with a cruel dilemma."
    } ]
  }, {
    "tStartMs": 23704,
    "dDurationMs": 6584,
    "segs": [ {
      "utf8": "He’ll ask each gingerbread man whether\nhe’d opt to Spare or Sacrifice the other."
    } ]
  }, {
    "tStartMs": 30288,
    "dDurationMs": 1416,
    "segs": [ {
      "utf8": "They can discuss,"
    } ]
  }, {
    "tStartMs": 31704,
    "dDurationMs": 5292,
    "segs": [ {
      "utf8": "but neither will know what the other\nchose until their decisions are locked in."
    } ]
  }, {
    "tStartMs": 36996,
    "dDurationMs": 6708,
    "segs": [ {
      "utf8": "If both choose to spare the other, the fox\nwill eat just one of each of their limbs;"
    } ]
  }, {
    "tStartMs": 43704,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "if one chooses to spare \nwhile the other sacrifices,"
    } ]
  }, {
    "tStartMs": 47704,
    "dDurationMs": 2125,
    "segs": [ {
      "utf8": "the sparer will be fully eaten,"
    } ]
  }, {
    "tStartMs": 49829,
    "dDurationMs": 4208,
    "segs": [ {
      "utf8": "while the traitor will run away\nwith all his limbs intact."
    } ]
  }, {
    "tStartMs": 54037,
    "dDurationMs": 6792,
    "segs": [ {
      "utf8": "Finally, if both choose to sacrifice,\nthe fox will eat 3 limbs from each."
    } ]
  }, {
    "tStartMs": 61329,
    "dDurationMs": 4709,
    "segs": [ {
      "utf8": "In game theory, this scenario \nis called the “Prisoner's Dilemma.”"
    } ]
  }, {
    "tStartMs": 66038,
    "dDurationMs": 4750,
    "segs": [ {
      "utf8": "To figure out how these gingerbread men \nwill act in their perfect rationality,"
    } ]
  }, {
    "tStartMs": 70788,
    "dDurationMs": 3375,
    "segs": [ {
      "utf8": "we can map the outcomes of each decision."
    } ]
  }, {
    "tStartMs": 74163,
    "dDurationMs": 4791,
    "segs": [ {
      "utf8": "The rows represent Crispy’s choices,\nand the columns are Chewy’s."
    } ]
  }, {
    "tStartMs": 78954,
    "dDurationMs": 2334,
    "segs": [ {
      "utf8": "Meanwhile, the numbers in each cell"
    } ]
  }, {
    "tStartMs": 81288,
    "dDurationMs": 2458,
    "segs": [ {
      "utf8": "represent the outcomes \nof their decisions,"
    } ]
  }, {
    "tStartMs": 83746,
    "dDurationMs": 3458,
    "segs": [ {
      "utf8": "as measured in the number \nof limbs each would keep:"
    } ]
  }, {
    "tStartMs": 87204,
    "dDurationMs": 4375,
    "segs": [ {
      "utf8": "So do we expect their friendship \nto last the game?"
    } ]
  }, {
    "tStartMs": 91579,
    "dDurationMs": 2750,
    "segs": [ {
      "utf8": "First, let’s consider Chewy’s options."
    } ]
  }, {
    "tStartMs": 94329,
    "dDurationMs": 5167,
    "segs": [ {
      "utf8": "If Crispy spares him, Chewy can run\naway scot-free by sacrificing Crispy."
    } ]
  }, {
    "tStartMs": 99496,
    "dDurationMs": 2042,
    "segs": [ {
      "utf8": "But if Crispy sacrifices him,"
    } ]
  }, {
    "tStartMs": 101538,
    "dDurationMs": 4750,
    "segs": [ {
      "utf8": "Chewy can keep one of his limbs\nif he also sacrifices Crispy."
    } ]
  }, {
    "tStartMs": 106288,
    "dDurationMs": 2375,
    "segs": [ {
      "utf8": "No matter what Crispy decides,"
    } ]
  }, {
    "tStartMs": 108663,
    "dDurationMs": 6250,
    "segs": [ {
      "utf8": "Chewy always experiences the best outcome\nby choosing to sacrifice his companion."
    } ]
  }, {
    "tStartMs": 114913,
    "dDurationMs": 2458,
    "segs": [ {
      "utf8": "The same is true for Crispy."
    } ]
  }, {
    "tStartMs": 117371,
    "dDurationMs": 3375,
    "segs": [ {
      "utf8": "This is the standard conclusion\nof the Prisoner's Dilemma:"
    } ]
  }, {
    "tStartMs": 120746,
    "dDurationMs": 2583,
    "segs": [ {
      "utf8": "the two characters will\nbetray one another."
    } ]
  }, {
    "tStartMs": 123329,
    "dDurationMs": 4250,
    "segs": [ {
      "utf8": "Their strategy to unconditionally\nsacrifice their companion"
    } ]
  }, {
    "tStartMs": 127579,
    "dDurationMs": 4209,
    "segs": [ {
      "utf8": "is what game theorists\ncall the “Nash Equilibrium,\""
    } ]
  }, {
    "tStartMs": 131788,
    "dDurationMs": 3958,
    "segs": [ {
      "utf8": "meaning that neither can gain\nby deviating from it."
    } ]
  }, {
    "tStartMs": 135746,
    "dDurationMs": 2375,
    "segs": [ {
      "utf8": "Crispy and Chewy act accordingly"
    } ]
  }, {
    "tStartMs": 138121,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "and the smug fox runs off \nwith a belly full of gingerbread,"
    } ]
  }, {
    "tStartMs": 142121,
    "dDurationMs": 4458,
    "segs": [ {
      "utf8": "leaving the two former friends\nwith just one leg to stand on."
    } ]
  }, {
    "tStartMs": 146579,
    "dDurationMs": 2750,
    "segs": [ {
      "utf8": "Normally, this is where\nthe story would end,"
    } ]
  }, {
    "tStartMs": 149329,
    "dDurationMs": 3834,
    "segs": [ {
      "utf8": "but a wizard happened to be watching\nthe whole mess unfold."
    } ]
  }, {
    "tStartMs": 153163,
    "dDurationMs": 4791,
    "segs": [ {
      "utf8": "He tells Crispy and Chewy that, \nas punishment for betraying each other,"
    } ]
  }, {
    "tStartMs": 157954,
    "dDurationMs": 4125,
    "segs": [ {
      "utf8": "they’re doomed to repeat this dilemma\nfor the rest of their lives,"
    } ]
  }, {
    "tStartMs": 162079,
    "dDurationMs": 4500,
    "segs": [ {
      "utf8": "starting with all four limbs\nat each sunrise."
    } ]
  }, {
    "tStartMs": 166579,
    "dDurationMs": 1834,
    "segs": [ {
      "utf8": "Now what happens?"
    } ]
  }, {
    "tStartMs": 168413,
    "dDurationMs": 5708,
    "segs": [ {
      "utf8": "This is called an Infinite Prisoner’s \nDilemma, and it’s a literal game changer."
    } ]
  }, {
    "tStartMs": 174121,
    "dDurationMs": 4458,
    "segs": [ {
      "utf8": "That’s because the gingerbread men \ncan now use their future decisions"
    } ]
  }, {
    "tStartMs": 178579,
    "dDurationMs": 3209,
    "segs": [ {
      "utf8": "as bargaining chips for the present ones."
    } ]
  }, {
    "tStartMs": 181788,
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    "segs": [ {
      "utf8": "Consider this strategy: both agree \nto spare each other every day."
    } ]
  }, {
    "tStartMs": 186496,
    "dDurationMs": 2917,
    "segs": [ {
      "utf8": "If one ever chooses to sacrifice,"
    } ]
  }, {
    "tStartMs": 189413,
    "dDurationMs": 4208,
    "segs": [ {
      "utf8": "the other will retaliate by choosing \n“sacrifice” for the rest of eternity."
    } ]
  }, {
    "tStartMs": 193621,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "So is that enough to get these\npoor sentient baked goods"
    } ]
  }, {
    "tStartMs": 197621,
    "dDurationMs": 2125,
    "segs": [ {
      "utf8": "to agree to cooperate?"
    } ]
  }, {
    "tStartMs": 199746,
    "dDurationMs": 4667,
    "segs": [ {
      "utf8": "To figure that out, we have to factor\nin another consideration:"
    } ]
  }, {
    "tStartMs": 204413,
    "dDurationMs": 3166,
    "segs": [ {
      "utf8": "the gingerbread men probably care\nabout the future"
    } ]
  }, {
    "tStartMs": 207579,
    "dDurationMs": 2834,
    "segs": [ {
      "utf8": "less than they care about the present."
    } ]
  }, {
    "tStartMs": 210413,
    "dDurationMs": 2500,
    "segs": [ {
      "utf8": "In other words, they might discount"
    } ]
  }, {
    "tStartMs": 212913,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "how much they care about their future\nlimbs by some number,"
    } ]
  }, {
    "tStartMs": 216913,
    "dDurationMs": 2416,
    "segs": [ {
      "utf8": "which we’ll call delta."
    } ]
  }, {
    "tStartMs": 219329,
    "dDurationMs": 4792,
    "segs": [ {
      "utf8": "This is similar to the idea of inflation \neroding the value of money."
    } ]
  }, {
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    "segs": [ {
      "utf8": "If delta is one half,"
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  }, {
    "tStartMs": 226038,
    "dDurationMs": 5500,
    "segs": [ {
      "utf8": "on day one they care about day 2 limbs\nhalf as much as day 1 limbs,"
    } ]
  }, {
    "tStartMs": 231538,
    "dDurationMs": 4833,
    "segs": [ {
      "utf8": "day 3 limbs 1 quarter as much \nas day 1 limbs, and so on."
    } ]
  }, {
    "tStartMs": 236371,
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    "segs": [ {
      "utf8": "A delta of 0 means that they don’t care \nabout their future limbs at all,"
    } ]
  }, {
    "tStartMs": 241371,
    "dDurationMs": 4958,
    "segs": [ {
      "utf8": "so they’ll repeat their initial choice\nof mutual sacrifice endlessly."
    } ]
  }, {
    "tStartMs": 246329,
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    "segs": [ {
      "utf8": "But as delta approaches 1, \nthey’ll do anything possible"
    } ]
  }, {
    "tStartMs": 250579,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "to avoid the pain of infinite triple limb \nconsumption,"
    } ]
  }, {
    "tStartMs": 254579,
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    "segs": [ {
      "utf8": "which means they’ll choose\nto spare each other."
    } ]
  }, {
    "tStartMs": 257413,
    "dDurationMs": 3375,
    "segs": [ {
      "utf8": "At some point in between\nthey could go either way."
    } ]
  }, {
    "tStartMs": 260788,
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    "segs": [ {
      "utf8": "We can find out where that point is"
    } ]
  }, {
    "tStartMs": 262913,
    "dDurationMs": 4208,
    "segs": [ {
      "utf8": "by writing the infinite series \nthat represents each strategy,"
    } ]
  }, {
    "tStartMs": 267121,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "setting them equal to each other,\nand solving for delta."
    } ]
  }, {
    "tStartMs": 271121,
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    "segs": [ {
      "utf8": "That yields 1/3, meaning that as long\nas Crispy and Chewy care about tomorrow"
    } ]
  }, {
    "tStartMs": 276788,
    "dDurationMs": 3125,
    "segs": [ {
      "utf8": "at least 1/3 as much as today,"
    } ]
  }, {
    "tStartMs": 279913,
    "dDurationMs": 4375,
    "segs": [ {
      "utf8": "it’s optimal for them \nto spare and cooperate forever."
    } ]
  }, {
    "tStartMs": 284288,
    "dDurationMs": 3750,
    "segs": [ {
      "utf8": "This analysis isn’t unique\nto cookies and wizards;"
    } ]
  }, {
    "tStartMs": 288038,
    "dDurationMs": 2791,
    "segs": [ {
      "utf8": "we see it play out in real-life situations"
    } ]
  }, {
    "tStartMs": 290829,
    "dDurationMs": 3792,
    "segs": [ {
      "utf8": "like trade negotiations\nand international politics."
    } ]
  }, {
    "tStartMs": 294621,
    "dDurationMs": 4208,
    "segs": [ {
      "utf8": "Rational leaders must assume \nthat the decisions they make today"
    } ]
  }, {
    "tStartMs": 298829,
    "dDurationMs": 3250,
    "segs": [ {
      "utf8": "will impact those of their adversaries \ntomorrow."
    } ]
  }, {
    "tStartMs": 302079,
    "dDurationMs": 4584,
    "segs": [ {
      "utf8": "Selfishness may win out in the short-term,\nbut with the proper incentives,"
    } ]
  }, {
    "tStartMs": 306663,
    "dDurationMs": 6583,
    "segs": [ {
      "utf8": "peaceful cooperation is not only possible,\nbut demonstrably and mathematically ideal."
    } ]
  }, {
    "tStartMs": 313246,
    "dDurationMs": 4000,
    "segs": [ {
      "utf8": "As for the gingerbread men, \ntheir eternity may be pretty crumby,"
    } ]
  }, {
    "tStartMs": 317246,
    "dDurationMs": 2292,
    "segs": [ {
      "utf8": "but so long as they go out on a limb,"
    } ]
  }, {
    "tStartMs": 319538,
    "dDurationMs": 3000,
    "segs": [ {
      "utf8": "their friendship will never \nagain be half-baked."
    } ]
  } ]
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