How to outsmart the Prisoner's Dilemma
-
0:07 - 0:12Two perfectly rational gingerbread men,
Crispy and Chewy, -
0:12 - 0:15are out strolling
when they’re caught by a fox. -
0:15 - 0:18Seeing how happy they are,
he decides that, -
0:18 - 0:20instead of simply eating them,
-
0:20 - 0:24he’ll put their friendship
to the test with a cruel dilemma. -
0:24 - 0:30He’ll ask each gingerbread man whether
he’d opt to Spare or Sacrifice the other. -
0:30 - 0:32They can discuss,
-
0:32 - 0:37but neither will know what the other
chose until their decisions are locked in. -
0:37 - 0:44If both choose to spare the other, the fox
will eat just one of each of their limbs; -
0:44 - 0:48if one chooses to spare
while the other sacrifices, -
0:48 - 0:50the sparer will be fully eaten,
-
0:50 - 0:54while the traitor will run away
with all his limbs intact. -
0:54 - 1:01Finally, if both choose to sacrifice,
the fox will eat 3 limbs from each. -
1:01 - 1:06In game theory, this scenario
is called the “Prisoner's Dilemma.” -
1:06 - 1:11To figure out how these gingerbread men
will act in their perfect rationality, -
1:11 - 1:14we can map the outcomes of each decision.
-
1:14 - 1:19The rows represent Crispy’s choices,
and the columns are Chewy’s. -
1:19 - 1:21Meanwhile, the numbers in each cell
-
1:21 - 1:24represent the outcomes
of their decisions, -
1:24 - 1:27as measured in the number
of limbs each would keep: -
1:27 - 1:32So do we expect their friendship
to last the game? -
1:32 - 1:34First, let’s consider Chewy’s options.
-
1:34 - 1:39If Crispy spares him, Chewy can run
away scot-free by sacrificing Crispy. -
1:39 - 1:42But if Crispy sacrifices him,
-
1:42 - 1:46Chewy can keep one of his limbs
if he also sacrifices Crispy. -
1:46 - 1:49No matter what Crispy decides,
-
1:49 - 1:55Chewy always experiences the best outcome
by choosing to sacrifice his companion. -
1:55 - 1:57The same is true for Crispy.
-
1:57 - 2:01This is the standard conclusion
of the Prisoner's Dilemma: -
2:01 - 2:03the two characters will
betray one another. -
2:03 - 2:08Their strategy to unconditionally
sacrifice their companion -
2:08 - 2:12is what game theorists
call the “Nash Equilibrium," -
2:12 - 2:16meaning that neither can gain
by deviating from it. -
2:16 - 2:18Crispy and Chewy act accordingly
-
2:18 - 2:22and the smug fox runs off
with a belly full of gingerbread, -
2:22 - 2:27leaving the two former friends
with just one leg to stand on. -
2:27 - 2:29Normally, this is where
the story would end, -
2:29 - 2:33but a wizard happened to be watching
the whole mess unfold. -
2:33 - 2:38He tells Crispy and Chewy that,
as punishment for betraying each other, -
2:38 - 2:42they’re doomed to repeat this dilemma
for the rest of their lives, -
2:42 - 2:47starting with all four limbs
at each sunrise. -
2:47 - 2:48Now what happens?
-
2:48 - 2:54This is called an Infinite Prisoner’s
Dilemma, and it’s a literal game changer. -
2:54 - 2:59That’s because the gingerbread men
can now use their future decisions -
2:59 - 3:02as bargaining chips for the present ones.
-
3:02 - 3:06Consider this strategy: both agree
to spare each other every day. -
3:06 - 3:09If one ever chooses to sacrifice,
-
3:09 - 3:14the other will retaliate by choosing
“sacrifice” for the rest of eternity. -
3:14 - 3:18So is that enough to get these
poor sentient baked goods -
3:18 - 3:20to agree to cooperate?
-
3:20 - 3:24To figure that out, we have to factor
in another consideration: -
3:24 - 3:28the gingerbread men probably care
about the future -
3:28 - 3:30less than they care about the present.
-
3:30 - 3:33In other words, they might discount
-
3:33 - 3:37how much they care about their future
limbs by some number, -
3:37 - 3:39which we’ll call delta.
-
3:39 - 3:44This is similar to the idea of inflation
eroding the value of money. -
3:44 - 3:46If delta is one half,
-
3:46 - 3:52on day one they care about day 2 limbs
half as much as day 1 limbs, -
3:52 - 3:56day 3 limbs 1 quarter as much
as day 1 limbs, and so on. -
3:56 - 4:01A delta of 0 means that they don’t care
about their future limbs at all, -
4:01 - 4:06so they’ll repeat their initial choice
of mutual sacrifice endlessly. -
4:06 - 4:11But as delta approaches 1,
they’ll do anything possible -
4:11 - 4:15to avoid the pain of infinite triple limb
consumption, -
4:15 - 4:17which means they’ll choose
to spare each other. -
4:17 - 4:21At some point in between
they could go either way. -
4:21 - 4:23We can find out where that point is
-
4:23 - 4:27by writing the infinite series
that represents each strategy, -
4:27 - 4:31setting them equal to each other,
and solving for delta. -
4:31 - 4:37That yields 1/3, meaning that as long
as Crispy and Chewy care about tomorrow -
4:37 - 4:40at least 1/3 as much as today,
-
4:40 - 4:44it’s optimal for them
to spare and cooperate forever. -
4:44 - 4:48This analysis isn’t unique
to cookies and wizards; -
4:48 - 4:51we see it play out in real-life situations
-
4:51 - 4:55like trade negotiations
and international politics. -
4:55 - 4:59Rational leaders must assume
that the decisions they make today -
4:59 - 5:02will impact those of their adversaries
tomorrow. -
5:02 - 5:07Selfishness may win out in the short-term,
but with the proper incentives, -
5:07 - 5:13peaceful cooperation is not only possible,
but demonstrably and mathematically ideal. -
5:13 - 5:17As for the gingerbread men,
their eternity may be pretty crumby, -
5:17 - 5:20but so long as they go out on a limb,
-
5:20 - 5:23their friendship will never
again be half-baked.
- Title:
- How to outsmart the Prisoner's Dilemma
- Speaker:
- Lucas Husted
- Description:
-
View full lesson: https://ed.ted.com/lessons/how-to-outsmart-the-prisoner-s-dilemma-lucas-husted
Two perfectly rational gingerbread men, Crispy and Chewy, are out strolling when they're caught by a fox. Instead of simply eating them, he decides to put their friendship to the test with a cruel dilemma. He'll ask each gingerbread man whether he'd opt to Spare or Sacrifice the other. What should they choose? Lucas Husted dives into the classic game theory scenario: the Prisoner's Dilemma.
Lesson by Lucas Husted, directed by Ivana Bošnjack and Thomas Johnson.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 05:24
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Tara Ahmadinejad edited English subtitles for How to outsmart the Prisoner's Dilemma | ||
Tara Ahmadinejad edited English subtitles for How to outsmart the Prisoner's Dilemma |