[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.65,0:00:10.30,Default,,0000,0000,0000,,A few months ago we posed a challenge \Nto our community.
Dialogue: 0,0:00:10.30,0:00:15.19,Default,,0000,0000,0000,,We asked everyone: given a range of \Nintegers from 0 to 100,
Dialogue: 0,0:00:15.19,0:00:22.06,Default,,0000,0000,0000,,guess the whole number closest to 2/3 \Nof the average of all numbers guessed.
Dialogue: 0,0:00:22.06,0:00:26.78,Default,,0000,0000,0000,,So if the average of all guesses is 60, \Nthe correct guess will be 40.
Dialogue: 0,0:00:26.78,0:00:31.41,Default,,0000,0000,0000,,What number do you think was the \Ncorrect guess at 2/3 of the average?
Dialogue: 0,0:00:32.73,0:00:36.11,Default,,0000,0000,0000,,Let’s see if we can try and reason \Nour way to the answer.
Dialogue: 0,0:00:36.11,0:00:41.41,Default,,0000,0000,0000,,This game is played under conditions known\Nto game theorists as common knowledge.
Dialogue: 0,0:00:41.41,0:00:44.50,Default,,0000,0000,0000,,Not only does every player have \Nthe same information —
Dialogue: 0,0:00:44.50,0:00:46.71,Default,,0000,0000,0000,,they also know that everyone else does,
Dialogue: 0,0:00:46.71,0:00:52.62,Default,,0000,0000,0000,,and that everyone else knows that \Neveryone else does, and so on, infinitely.
Dialogue: 0,0:00:52.62,0:00:58.54,Default,,0000,0000,0000,,Now, the highest possible average would \Noccur if every person guessed 100.
Dialogue: 0,0:00:58.54,0:01:03.27,Default,,0000,0000,0000,,In that case, 2/3 of the average \Nwould be 66.66.
Dialogue: 0,0:01:03.27,0:01:05.20,Default,,0000,0000,0000,,Since everyone can figure this out,
Dialogue: 0,0:01:05.20,0:01:09.62,Default,,0000,0000,0000,,it wouldn’t make sense to guess \Nanything higher than 67.
Dialogue: 0,0:01:09.62,0:01:12.75,Default,,0000,0000,0000,,If everyone playing comes to \Nthis same conclusion,
Dialogue: 0,0:01:12.75,0:01:15.52,Default,,0000,0000,0000,,no one will guess higher than 67.
Dialogue: 0,0:01:15.52,0:01:19.66,Default,,0000,0000,0000,,Now 67 is the new highest \Npossible average,
Dialogue: 0,0:01:19.66,0:01:25.44,Default,,0000,0000,0000,,so no reasonable guess should be \Nhigher than ⅔ of that, which is 44.
Dialogue: 0,0:01:25.44,0:01:28.98,Default,,0000,0000,0000,,This logic can be extended further \Nand further.
Dialogue: 0,0:01:28.98,0:01:33.71,Default,,0000,0000,0000,,With each step, the highest possible \Nlogical answer keeps getting smaller.
Dialogue: 0,0:01:33.71,0:01:38.28,Default,,0000,0000,0000,,So it would seem sensible to guess the \Nlowest number possible.
Dialogue: 0,0:01:38.28,0:01:41.13,Default,,0000,0000,0000,,And indeed, if everyone chose zero,
Dialogue: 0,0:01:41.13,0:01:45.06,Default,,0000,0000,0000,,the game would reach what’s known \Nas a Nash Equilibrium.
Dialogue: 0,0:01:45.06,0:01:49.42,Default,,0000,0000,0000,,This is a state where every player has \Nchosen the best possible strategy
Dialogue: 0,0:01:49.42,0:01:52.52,Default,,0000,0000,0000,,for themselves given \Neveryone else playing,
Dialogue: 0,0:01:52.52,0:01:57.33,Default,,0000,0000,0000,,and no individual player can benefit \Nby choosing differently.
Dialogue: 0,0:01:57.33,0:02:01.51,Default,,0000,0000,0000,,But, that’s not what happens \Nin the real world.
Dialogue: 0,0:02:01.51,0:02:05.48,Default,,0000,0000,0000,,People, as it turns out, either aren’t \Nperfectly rational,
Dialogue: 0,0:02:05.48,0:02:09.04,Default,,0000,0000,0000,,or don’t expect each other \Nto be perfectly rational.
Dialogue: 0,0:02:09.04,0:02:12.37,Default,,0000,0000,0000,,Or, perhaps, it’s some combination \Nof the two.
Dialogue: 0,0:02:12.37,0:02:15.22,Default,,0000,0000,0000,,When this game is played in \Nreal-world settings,
Dialogue: 0,0:02:15.22,0:02:20.22,Default,,0000,0000,0000,,the average tends to be somewhere \Nbetween 20 and 35.
Dialogue: 0,0:02:20.22,0:02:26.08,Default,,0000,0000,0000,,Danish newspaper Politiken ran the game \Nwith over 19,000 readers participating,
Dialogue: 0,0:02:26.08,0:02:32.06,Default,,0000,0000,0000,,resulting in an average of roughly 22, \Nmaking the correct answer 14.
Dialogue: 0,0:02:32.06,0:02:35.76,Default,,0000,0000,0000,,For our audience, the average was 31.3.
Dialogue: 0,0:02:35.76,0:02:41.02,Default,,0000,0000,0000,,So if you guessed 21 as 2/3 of \Nthe average, well done.
Dialogue: 0,0:02:41.02,0:02:44.68,Default,,0000,0000,0000,,Economic game theorists have a \Nway of modeling this interplay
Dialogue: 0,0:02:44.68,0:02:49.80,Default,,0000,0000,0000,,between rationality and practicality \Ncalled k-level reasoning.
Dialogue: 0,0:02:49.80,0:02:54.64,Default,,0000,0000,0000,,K stands for the number of times a \Ncycle of reasoning is repeated.
Dialogue: 0,0:02:54.64,0:02:58.95,Default,,0000,0000,0000,,A person playing at k-level 0 would \Napproach our game naively,
Dialogue: 0,0:02:58.95,0:03:02.68,Default,,0000,0000,0000,,guessing a number at random without \Nthinking about the other players.
Dialogue: 0,0:03:02.68,0:03:07.88,Default,,0000,0000,0000,,At k-level 1, a player would assume \Neveryone else was playing at level 0,
Dialogue: 0,0:03:07.88,0:03:12.42,Default,,0000,0000,0000,,resulting in an average of 50, \Nand thus guess 33.
Dialogue: 0,0:03:12.42,0:03:17.19,Default,,0000,0000,0000,,At k-level 2, they’d assume that everyone \Nelse was playing at level 1,
Dialogue: 0,0:03:17.19,0:03:19.49,Default,,0000,0000,0000,,leading them to guess 22.
Dialogue: 0,0:03:19.49,0:03:23.10,Default,,0000,0000,0000,,It would take 12 k-levels to reach 0.
Dialogue: 0,0:03:23.10,0:03:27.92,Default,,0000,0000,0000,,The evidence suggests that most \Npeople stop at 1 or 2 k-levels.
Dialogue: 0,0:03:27.92,0:03:29.40,Default,,0000,0000,0000,,And that’s useful to know,
Dialogue: 0,0:03:29.40,0:03:34.00,Default,,0000,0000,0000,,because k-level thinking comes into \Nplay in high-stakes situations.
Dialogue: 0,0:03:34.00,0:03:39.38,Default,,0000,0000,0000,,For example, stock traders evaluate stocks\Nnot only based on earnings reports,
Dialogue: 0,0:03:39.38,0:03:43.11,Default,,0000,0000,0000,,but also on the value that others \Nplace on those numbers.
Dialogue: 0,0:03:43.11,0:03:45.40,Default,,0000,0000,0000,,And during penalty kicks in soccer,
Dialogue: 0,0:03:45.40,0:03:49.54,Default,,0000,0000,0000,,both the shooter and the goalie decide \Nwhether to go right or left
Dialogue: 0,0:03:49.54,0:03:52.74,Default,,0000,0000,0000,,based on what they think the other \Nperson is thinking.
Dialogue: 0,0:03:52.74,0:03:56.69,Default,,0000,0000,0000,,Goalies often memorize the patterns of \Ntheir opponents ahead of time,
Dialogue: 0,0:03:56.69,0:04:00.29,Default,,0000,0000,0000,,but penalty shooters know that \Nand can plan accordingly.
Dialogue: 0,0:04:00.29,0:04:03.55,Default,,0000,0000,0000,,In each case, participants must weigh \Ntheir own understanding
Dialogue: 0,0:04:03.55,0:04:07.74,Default,,0000,0000,0000,,of the best course of action against how \Nwell they think other participants
Dialogue: 0,0:04:07.74,0:04:10.14,Default,,0000,0000,0000,,understand the situation.
Dialogue: 0,0:04:10.14,0:04:14.92,Default,,0000,0000,0000,,But 1 or 2 k-levels is by no means \Na hard and fast rule—
Dialogue: 0,0:04:14.92,0:04:20.34,Default,,0000,0000,0000,,simply being conscious of this tendency \Ncan make people adjust their expectations.
Dialogue: 0,0:04:20.34,0:04:24.36,Default,,0000,0000,0000,,For instance, what would happen \Nif people played the 2/3 game
Dialogue: 0,0:04:24.36,0:04:28.25,Default,,0000,0000,0000,,after understanding the difference between\Nthe most logical approach
Dialogue: 0,0:04:28.25,0:04:29.85,Default,,0000,0000,0000,,and the most common?
Dialogue: 0,0:04:29.85,0:04:34.29,Default,,0000,0000,0000,,Submit your own guess at what 2/3 \Nof the new average will be
Dialogue: 0,0:04:34.29,0:04:36.23,Default,,0000,0000,0000,,by using the form below,
Dialogue: 0,0:04:36.23,0:04:37.81,Default,,0000,0000,0000,,and we’ll find out.