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This is a video about the most famous problem in game theory.
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Problems of this sort pop up everywhere, from nations locked in conflict to roommates doing the dishes.
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Even game shows have been based around this concept.
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Figuring out the best strategy can mean the difference between life and death, war and peace, flourishing and the destruction of the planet.
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And in the mechanics of this game, we may find the very source of one of the most first, unexpected phenomena in nature, cooperation.
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On the 3rd of September 1949, an American weather monitoring plane collected air samples over Japan.
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In those samples, they found traces of radioactive material.
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The Navy quickly collected and tested rainwater samples from their ships and bases all over the world.
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They also detected small amounts of cerium -141 and yttrium -91.
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But these isotopes have half -lives of one or two months, so they must have been produced recently.
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And the only place they could have come from was a nuclear explosion.
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But the U .S hadn't performed any tests that year,
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so the only possible conclusion was that the Soviet Union had figured out how to make a nuclear bomb.
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This was the news the Americans had been dreading.
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Their military supremacy, achieved through the Manhattan Project, was quickly fading.
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This makes the problem of Western Europe and the United States far more serious than it was before, and perhaps makes the imminence of war greater.
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Some thought their best course of action was to launch an unprovoked nuclear strike against the Soviets while they were still ahead.
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In the words of Navy Secretary Matthews, to become aggressors for peace.
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John von Neumann, the founder of Game Theory, said, If you say, why not bomb them tomorrow, I say, why not bomb them today?
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If you say today at five o 'clock, I say, why not at one o 'clock?
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Something needed to be done about nuclear weapons and fast. But what?
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In 1950, the Rand Corporation, a US -based think tank, was studying this question, and as part of this research, they turned to game theory.
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That same year, two mathematicians at RAND had invented a new game, one which, unbeknownst to them at the time, closely resembled the U .S.-Soviet conflict.
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This game is now known as the Prisoner's Dilemma, so let's play a game.
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A banker with a chest full of gold coins invites you
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and another player to play against each other you each get two choices.
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You can cooperate, or you can defect.
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If you both cooperate, you each get three coins.
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If one of you cooperates, but the other defects, then the one who defected gets five coins, and the other gets nothing.
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And if you both defect, then you each get a coin.
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The goal of the game is simple, to get as many coins as you can.
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So, what would you do?
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Suppose your opponent cooperates, then you could also cooperate and get 3 coins.
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Or you could defect and get 5 coins instead, so you are better off defecting.
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But what if your opponent defects instead?
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Well, you could cooperate and get no coins, or you could defect and at least get 1 coin.
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So no matter what your opponent does, your best option is always to defect.
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Now if your opponent is also rational, they will reach the same conclusion and therefore also defect.
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As a result, when you both act rationally, you both end up in the suboptimal situation getting one coin each, when you could have gotten three instead.
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In the case of the US and Soviet Union, this led both countries to develop huge nuclear arsenals of tens of thousands of nuclear weapons each,
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more than enough to destroy each other many times over.
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But since both countries had nukes, neither could use them.
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And both countries spent around 10 trillion dollars developing these weapons.
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Both would have been better off if they had cooperated and agreed not to develop this technology further.
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But since they both acted in their own best interest, they ended up in a situation where everyone was worse off.
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The Prisoner's Dilemma is one of the most famous games in game theory.
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Thousands and thousands of papers have been published on versions of this game.
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In part, that's because it pops up everywhere.
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Impalas living in between African woodlands and savannas are prone to catching ticks, which can lead to infectious diseases, paralysis, even death.
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So it's important for impalas to remove ticks, and they do this by grooming.
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But they can't reach all the spots on their bodies, and therefore they need another impala to groom them.
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Now, grooming someone else comes at a cost.
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It costs saliva, electrolytes, time and attention, all vital resources under the hot African sun, where a predator could strike at any moment.
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So for the other impala, it would be best not to pay this cost.
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But then again, it too will need help grooming.
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So all Impalas face a choice.
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Should they groom each other or not?
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In other words, should they cooperate or defect?
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Well, if they only interact once, then the rational solution is always to defect.
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That other Impala is never going to help you, so why bother?
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But the thing about a lot of problems is that they're not a single prisoner's dilemma.
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Impalas see each other day after day, and the same situation keeps happening over and over again.
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So that changes the problem.
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Because instead of playing the Prisoner's Dilemma just once, you're now playing it many, many times.
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And if I defect now, then my opponent will know that I defected, and they can use that against me in the future.
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So, what is the best strategy in this repeated game?
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That is what Robert Axelrod, a political scientist, wanted to find out.
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So in 1980, he decided to hold a computer tournament.
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He invited some of the world's leading game theorists from many different subjects to submit computer programs that would play each other.
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Axelrod called these programs strategies strategies.
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Each strategy would face off against every other strategy and against a copy of itself.
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And each matchup would go for 200 rounds.
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That's important, and we'll come back to it.
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Now Axelrod used points instead of coins, but the payoffs were the same.
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The goal of the tournament was to win as many points as possible.
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And in the end, the whole tournament was repeated five times over to ensure the success was robust
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and not just a fluke.
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Axelrod gave an example of a simple strategy.
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It would start each game by cooperating, and only defect after its opponent had defected twice in a row.
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In total, Axelrod received 14 strategies, and he added a 15th called Random, which just randomly cooperates or defects 50 % of the time.
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All strategies were loaded onto a single computer, where they faced off against each other.
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One of the strategies was called Freedmen.
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It starts off by cooperating, but if its opponent defects just once, it will keep defecting for the remainder of the game.
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Another strategy was called Joss.
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It also starts by cooperating, but then it just copies what the other player did on the last move.
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Then around 10 % of the time, Joss gets sneaky and defects.
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There was also a rather elaborate strategy called Grass Camp.
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This strategy works the same as Joss, but instead of defecting probabilistically, grass -camped effects in the 50th round to try
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and probe the strategy of its opponent and see if it can take advantage of any weaknesses.
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The most elaborate strategy was name withheld with 77 lines of code.
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After all the games were played, the results were tallied up and the leaderboard established.
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The crazy thing was that the simplest program ended up winning, a program that came to be called tit -for -tat.
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Tit -for -tat starts by cooperating, and then it copies exactly what its opponent did in the last move.
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So it would follow cooperation with cooperation, and defection with defection.
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But only once, if its opponent goes back to cooperating, so does tit -for -tat.
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When tit -for -tat played against Friedman, both started by cooperating, and they kept cooperating, both ending up with perfect scores for complete cooperation.
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When tit -for -tat played against Joss, they too started by cooperating, but then on the sixth move, Joss defected.
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This sparked a series of back and forth defections, a sort of echo effect.
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Okay, so now you've got this alternating thing, which will remind you of some of the politics of the world today, where we have to do something to you because of what you did to us.
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And then when this weird program throws in a second unprovoked defection,
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now it's really bad because now both programs are going to defect on each other for the rest of the game.
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And that's also like some of the things that we're seeing in politics today and in international relations.
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As a result of these mutual retaliations, both Tit for Tat and Joss did poorly.
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But because Tit for Tat managed to cooperate with enough other strategies, it still won the tournament.
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Hey my god, there's Professor Axelrod!
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Hey!
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There's Stephen Stewart!
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What a treat this is.
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And I imagined initially it'd be sort of like computer chess
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where you'd need a pretty complicated program to play a sophisticated game, but in fact it was not like that at all.
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It was the simplest strategy that did the best.
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So I analyzed how that happened.
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Axelrod found that all the best performing strategies, including tit -for -tat, shared four qualities.
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First, they were all nice, which just means they are not the first to defect.
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So tit -for -tat is a nice strategy.
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It can defect, but only in retaliation.
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The opposite of nice is nasty.
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That's a strategy that defects first.
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So Joss is nasty.
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Out of the 15 strategies in the tournament, 8 were nice and 7 nasty.
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The top 8 strategies were all nice.
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And even the worst -performing nice strategy still far outscored the best -performing nasty one.
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The second important quality was being forgiving.
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A forgiving strategy is one that can retaliate, but it doesn't hold a grudge.
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So tit -for -tat is a forgiving strategy.
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It retaliates when its opponent defects, but it doesn't let defections from before the last round influence its current decisions.
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Friedman, on the other hand, is maximally unforgiving.
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After the first defection, just from the opponent would defect for the rest of the game.
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Okay, that's it.
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No mercy.
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And that might feel good to do, but it doesn't end up working out well in the long run.
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This conclusion, that it pays to be nice and forgiving, came as a shock to the experts.
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Many had tried to be tricky and create subtle, nasty strategies to beat their opponent and eke out an advantage.
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But they all failed.
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Instead, in this tournament, nice guys finished first.
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Now, tit for tat is quite forgiving, but it's possible to be even more forgiving.
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Axelrod's sample strategy only defects after its opponent defected twice in a row.
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It was tit for two tats.
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Now, that might sound overly generous, but when Axelrod ran the numbers, he found that if anyone had submitted the sample strategy, they would have won the tournament.
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I mean, it's so clever.
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There's so many layers to this story.
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After Axelrod published his analysis of what happened, or circulated it among these game theorists,
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he said, now that we all know what worked well, let's try again.
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So he announced a second tournament where everything would be the same except for one change, the number of rounds per game.
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See, in the first tournament, each game lasted precisely 200 rounds and that is important because
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if you know when the last round is then there's no reason to cooperate in
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that round so you're better off defecting of course your opponent should reason the same
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and so they should also defect in the last round but
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if you both anticipate defection in the last round then there's
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no reason for you to cooperate in the second to last round
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or the round before that or before that and
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so on all the way to the very first round and so in In Axelrod's tournament, it was a very important thing that the players didn't know exactly how long they were going to be playing.
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They knew on average it would be 200 rounds, but there was a random number generator that prevented them from knowing with certainty.
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Yeah, if you're not sure when it ends, then you have to kind of keep cooperating because it might keep going and you might need them on your side.
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For this second tournament, Axelrod received 62 entries and again added random.
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The contestants had gotten the results and analysis from the first tournament and could use this information to their advantage.
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This created two camps.
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Some thought that clearly being nice and forgiving were winning qualities, so they submitted nice and forgiving strategies.
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One even submitted tit for two tats.
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The second camp anticipated that others would be nice and extra forgiving.
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Therefore, they submitted nasty strategies to try to take advantage of those that were extra forgiving.
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One such strategy was called Tester.
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It would defect on the first move to see how its opponent reacted.
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If it retaliated, Tester would apologize and play tit for tat for the remainder of the game.
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If it didn't retaliate, Tester would defect every other move after that.
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But again, being nasty didn't pay.
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And once again, tit for tat was the most effective.
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Nice strategies again did much better.
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In the top 15, only one was not nice.
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Similarly, in the bottom 15, only one was not nasty.
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After the second tournament, Axelrod identified the other qualities that distinguished the better performing strategies.
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The third is being retaliatory, which means if your opponent defects, strike back immediately.
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Don't be a pushover.
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Always cooperate is a total pushover, and so it's very easy to take advantage of.
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Tit for tat, on the other hand, is very hard to take advantage of.
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The last quality that Axelrod identified is being clear.
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Programs that were too opaque, that were too similar to a random program, you couldn't figure them out because they were so complicated.
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It was very hard to establish any pattern of trust with a program like
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that because you couldn't figure out what it was doing.
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I mean, the other programs it was playing couldn't figure them out.
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And so they would end up more or less defaulting to thinking, saying, every turn is like the last time I'm going to see you, so I might as well defect.
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What to me is mind -blowing about this is that these four principles,
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being nice, forgiving, provocable, and clear,
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is a lot like the morality that has evolved around the world that is often summarized as an eye for an eye.
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It's not Christianity, by the way.
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It's not turn the other cheek philosophy.
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It's some older philosophy.
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What's interesting is that while tit for two tats would have won the first tournament, it only came 24th in the second tournament.
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This highlights an important fact.
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In the repeated prisoner's dilemma, there is no single best strategy.
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The strategy that performs best always depends on the other strategies it's interacting with.
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For example, if you put tit for tat in an environment with only the ultimate bullies of always defect, then tit -for -tat comes in last.
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I wanted to see whether, for example, the tit -for -tat did well
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because it did well with really stupid rules that didn't do well at all themselves, that basically it took advantage of people.
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So he ran a simulation where successful strategies in one generation would see their numbers grow
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and unsuccessful ones would see their numbers drop.
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In this simulation, the worst performing strategies quickly shrink and go extinct, while the top -performing strategies become more common.
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Harrington, the only nasty strategy in the top 15, first grew quickly.
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But then as the strategies it was preying on went extinct, Harrington's numbers also quickly dropped.
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This shows a main benefit of this simulation because it tests how well a strategy does with other successful strategies.
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After a thousand generations, the proportions are mostly stable and only nice strategies survive.
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Again, tit for tat comes out on top, representing 14 .5 % of the total population.
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Now, this process may sound similar to evolution, but there is a subtle difference, which is that in this case, there are no mutations.
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So it's actually an ecological simulation.
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But what if the world you started in was different?
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Imagine a world that is a really nasty place to live, more or less populated with players
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that always defect except there's a little cluster of tit -for -tat players
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that live in some kind of nucleus
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and they get to play with each other a lot
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because they're geographically sequestered they will start building up a lot of points
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and also because that translates into offspring they'll start to take over the population
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so in fact Axelrod showed that a little island of cooperation can emerge
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and spread and eventually will take over the world which is fantastic
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How can cooperation emerge in a population of players who are self -interested,
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who are not trying to be good because they're good -hearted?
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You don't have to be altruistic.
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You could be looking out for number one for yourself and your own interests, and yet cooperation can still emerge.
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Some argue that this could explain how we went from a world full of completely selfish organisms, where every organism only cared about themselves,
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to one where cooperation emerged and flourished, from impalas grooming each other to fish cleaning sharks.
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Many lifeforms experience conflicts similar to the prisoner's dilemma, but because they don't interact just once,
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both can be better off by cooperating.
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And this doesn't require trust or conscious thought either, because the strategy could be encoded in DNA.
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As long as it performs better than the other strategies, it can take over a population.
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Axelrod's insights were applied to areas like evolutionary biology and international But there was one aspect that his original tournaments didn't cover.
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What happens if there is a little bit of random error in the game?
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Some noise in the system?
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For example, one player tries to cooperate, but it comes across as a defection.
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Little errors like this happen in the real world all the time.
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Like in 1983, the Soviet satellite -based early warning system detected the launch of an intercontinental ballistic missile from the U .S.
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But the U .S hadn't launched anything.
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The Soviet system had confused sunlight reflecting off high -altitude clouds with a ballistic missile.
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Thankfully, Stanislav Petrov, the Soviet officer on duty, dismissed the alarm.
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But this example shows the potential costs of a signal error
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and the importance of studying the effects of noise on those strategies.
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The word game sounds like it's a children's game or, you know, there's something, a misnomer maybe in calling it game theory,
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because these are life and death matters, obviously.
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And as you mentioned that this came up in the Cold War, I mean, it could actually be life and death of the whole planet.
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We could annihilate human civilization.
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So these are not games in any kind of trivial sense.
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It's just the term that is used by mathematicians and theorists.
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When tit -for -tat plays against itself in a noisy environment, both start off by cooperating.
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But if a single cooperation is perceived as a defection, then the other tit -for -tat retaliates, and it sets off a chain of alternating retaliations.
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And if another cooperation is perceived as a defection, then the rest of the game is constant mutual defection.
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Therefore, in the long run, both would only get a third of the points they would get in a perfect environment.
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Tit for tat goes from performing very well to performing poorly.
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So how do you solve this?
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Well, you need a reliable way to break out of these echo effects.
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And one way to do this is by playing tit for tat, but with around 10 % more forgiveness.
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So instead of retaliating after every defection, you only retaliate around 9 out of every 10 times.
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This helps you break out of those echoes while still being retaliatory enough to not be taken advantage of.
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And so we also ran the tournament with noise and generosity.
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And that did quite well.
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My favorite example is Tit for Tat does really well, but it could never do better than the player it's playing with.
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I mean, think about it.
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By design, all they can do is lose or draw.
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And yet, when the results of all interactions are tallied up, they come out ahead of all other strategies.
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Similarly, always defect can never lose a game.
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It can only draw or win.
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But overall, it performs extremely poorly.
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This highlights a common misconception.
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Because for many people, when they think about winning, they think they need to beat the other person.
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In games like chess or poker, this is true, since one person's gain is necessarily another person's loss, so these games are zero -sum.
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But most of life is not zero -sum.
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To win you don't need to get your reward from the other player, instead you can get it from the banker.
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Only in real life the banker is the world, it is literally everything around you.
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It is just up to us to find those win -win situations and then work together to unlock those rewards.
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Cooperation pays, even among rivals.
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From 1950 to 1986, the US and Soviet Union had trouble cooperating, and both kept developing nukes.
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But then, from the late 80s onwards, they started reducing their nuclear stockpiles.
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They too had learned how to resolve conflict.
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Rather than making an agreement to abolish all nuclear arms at once and essentially turning it into a single prisoner's dilemma,
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they would disarm slowly a small number of nukes each year, and then they'd check each other to see that they had both cooperated, and then repeat the year after,
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and the year after that, all along checking to ensure mutual cooperation.
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In the more than 40 years since Axelrod's tournaments, researchers have continued to study which strategies perform best in a variety of environments.
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In doing so, they varied everything from payoff structures to strategies to errors and more.
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Some even allowed the strategies to mutate.
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While tit for tat or generous tit for tat doesn't always come out on top, Axelrod's main takeaways still hold.
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Be nice, forgiving, but don't be a pushover.
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Can I ask you, why did Anatole Rappaport submit tit for tat?
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well the reason was because I asked him to
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and he he wrote saying yeah I'm going to do that
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but I just want to be clear that I'm not sure
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that this is really such a good idea I don't he was a peace researcher
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and I think his own inclinations were to be much more forgiving and maybe and not be so provokable.
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What I find fascinating is that one of the main things
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that sets life apart from non -living things is that life gets to make decisions.
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We get to make choices, choices that don't only change our future, but also the future of those we interact with.
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See, in the short term, it is often the environment that shapes the player, that determines who does well.
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But in the long run, it is the players that shape the environment
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so let's play a game the game of life
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and make your choices wisely
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because their impact may reach further than you think using the right strategy matters
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but figuring out the best strategy isn't easy it requires critical thinking and innovative solutions like Axelrod's tournaments.
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If you're looking for an easy way to build your problem solving skills then check out this video's sponsor Brilliant.
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All you need to do is set your learning goal and Brilliant will design the perfect path for you, equipping you with all the tools you need to reach it.
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Whether you're a budding statistician or you just want to learn about randomness and chance.
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This course will equip you with the skills you need to make decisions in uncertain situations.
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Từ vựng và ghi chú luyện nói cho bài học này
Video này có 311 câu và 4323 từ để luyện shadowing. Phần lời nói dài 27:16. Người nói nói với tốc độ tự nhiên, khoảng 159 từ mỗi phút, gần với hội thoại hằng ngày. Chỉ 81% số từ nằm trong 3.000 từ tiếng Anh thông dụng nhất, nên từ vựng khá khó.
Từ vựng quan trọng trong video
15 từ đáng học trong video, kèm phiên âm và nghĩa:
| Từ | Phiên âm | Nghĩa |
|---|---|---|
| defect danh từ | /ˈdiːfɛkt/ | tật, lỗi |
| cooperation danh từ | /koʊˌɑ.pəˈɹeɪ.ʃən/ | sự hợp tác, hợp tác |
| coin danh từ | /ˈkoɪ̯n/ | đồng tiền |
| cooperate động từ | /kəʊˈɒp.ə.ɹeɪt/ | cộng tác |
| submit động từ | /səbˈmɪt/ | đệ trình, nộp |
| interact động từ | /ɪn.təˈɹækt/ | tương tác |
| conclusion danh từ | /kənˈkluːʒən/ | kết thúc |
| probability danh từ | /ˌpɹɑ.bəˈbɪl.ə.ti/ | xác suất, khả năng |
| banker danh từ | /ˈbæŋkəː/ | chủ ngân hàng, chủ nhà băng |
| complicated tính từ | /ˈkɑm.plɪˌkeɪ.tɪd/ | phức tạp |
| solve động từ | /sɒlv/ | giải quyết |
| grass danh từ | /ɡɹɑːs/ | cỏ |
| reward danh từ | /ɹɪˈwɔɹd/ | tặng thưởng, thưởng |
| generous tính từ | /ˈd͡ʒɛn(ə)ɹəs/ | rộng lượng, hào phóng |
| insight danh từ | /ˈɪnsaɪ̯t/ | sự sáng suốt |
Cụm động từ bạn sẽ nghe
| Từ | Nghĩa |
|---|---|
| check out động từ | tính tiền, trả phòng |
Ngữ pháp trong video
Những cấu trúc người nói dùng nhiều nhất, kèm đúng cụm từ trong video:
| Cấu trúc | Trong video |
|---|---|
| Câu điều kiện if + mệnh đề, will/would + động từ — điều kiện và kết quả | If it retaliated, Tester would apologize · If it didn't retaliate, Tester would defect |
| Câu bị động be + quá khứ phân từ — nhấn vào việc xảy ra, không phải người làm | have been based · have been produced · be done |
| Mệnh đề quan hệ who / which + mệnh đề — thêm thông tin về người hoặc vật | one who defected · ticks, which can · thing, which will |
| Thì hiện tại hoàn thành have/has + quá khứ phân từ — việc đã xảy ra nhưng còn liên quan đến hiện tại | have been based · have been published · has evolved |
Phát âm cần chú ý
Người nói dùng 47 dạng rút gọn, ví dụ don't, you're, didn't. Hãy nói theo dạng ngắn đúng như bạn nghe.
- Âm “th”: mathematics /mæθ(.ə)ˈmæt.ɪks/, bother /ˈbɑðɚ/, sixth /sɪksθ/
- Âm “sh” và “zh”: cooperation /koʊˌɑ.pəˈɹeɪ.ʃən/, simulation /ˌsɪm.jəˈleɪ.ʃn̩/, conclusion /kənˈkluːʒən/, rational /ˈɹæʃ(ə)nəl/, establish /ɪˈstæb.lɪʃ/
- Từ dài — đặt trọng âm cho đúng: cooperation /koʊˌɑ.pəˈɹeɪ.ʃən/, cooperate /kəʊˈɒp.ə.ɹeɪt/, probability /ˌpɹɑ.bəˈbɪl.ə.ti/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, similarly /ˈsɪm.ə.lə.li/
Cách luyện với video này
- Nghe hết video một lần, chưa cần nói, và ghi lại những từ bạn chưa biết.
- Bắt đầu ở tốc độ 0,75×, nói đuổi từng câu, rồi quay lại tốc độ bình thường khi đã quen.
- Ghi âm giọng mình rồi so với bản gốc, chú ý các từ như defect, cooperation, coin.
Phương Pháp Shadowing Là Gì?
Shadowing là kỹ thuật học ngôn ngữ có cơ sở khoa học, ban đầu được phát triển cho chương trình đào tạo phiên dịch viên chuyên nghiệp và được phổ biến rộng rãi bởi nhà đa ngôn ngữ học Dr. Alexander Arguelles. Nguyên lý cốt lõi đơn giản nhưng cực kỳ hiệu quả: bạn nghe tiếng Anh của người bản xứ và lặp lại to ngay lập tức — như một "cái bóng" (shadow) đuổi theo người nói với độ trễ chỉ 1–2 giây. Khác với luyện ngữ pháp hay học từ vựng bị động, Shadowing buộc não bộ và cơ miệng phải đồng thời xử lý và tái tạo ngôn ngữ thực tế. Các nghiên cứu khoa học xác nhận phương pháp này cải thiện đáng kể phát âm, ngữ điệu, nhịp điệu, nối âm, kỹ năng nghe và độ lưu loát khi nói — đặc biệt hiệu quả cho người luyện IELTS Speaking và muốn giao tiếp tiếng Anh tự nhiên như người bản ngữ.