Name: How to outsmart the Prisoner’s Dilemma - Lucas Husted
Uploaded: 2020-10-26T18:26:06.000Z
Duration: 5 min 45 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Two perfectly rational gingerbread men, Crispy and Chewy,

are out strolling  when they're caught by a fox.

Seeing how happy they are,  he decides that,

he'll 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.

but neither will know what the other chose until their decisions are locked in.

If both choose to spare the other, the fox will eat just one of each of their limbs;

if one chooses to spare  while the other sacrifices,

while the traitor will run away with all his limbs intact.

Finally, if both choose to sacrifice, the fox will eat 3 limbs from each.

In game theory, this scenario  is called the “Prisoner's Dilemma.”

To figure out how these gingerbread men  will act in their perfect rationality,

we can map the outcomes of each decision.

The rows represent Crispy's choices, and the columns are Chewy's.

represent the outcomes  of their decisions,

as measured in the number  of limbs each would keep:

So do we expect their friendship  to last the game?

If Crispy spares him, Chewy can run away scot-free by sacrificing Crispy.

Chewy can keep one of his limbs if he also sacrifices Crispy.

Chewy always experiences the best outcome by choosing to sacrifice his companion.

This is the standard conclusion of the Prisoner's Dilemma:

the two characters will betray one another.

Their strategy to unconditionally sacrifice their companion

is what game theorists call the “Nash Equilibrium,"

meaning that neither can gain by deviating from it.

and the smug fox runs off  with a belly full of gingerbread,

leaving the two former friends with just one leg to stand on.

Normally, this is where the story would end,

but a wizard happened to be watching the whole mess unfold.

He tells Crispy and Chewy that,  as punishment for betraying each other,

they're doomed to repeat this dilemma for the rest of their lives,

starting with all four limbs at each sunrise.

This is called an Infinite Prisoner's  Dilemma, and it's a literal game changer.

That's because the gingerbread men  can now use their future decisions

as bargaining chips for the present ones.

Consider this strategy: both agree  to spare each other every day.

the other will retaliate by choosing  “sacrifice” for the rest of eternity.

So is that enough to get these poor sentient baked goods

To figure that out, we have to factor in another consideration:

the gingerbread men probably care about the future

how much they care about their future limbs by some number,

This is similar to the idea of inflation  eroding the value of money.

on day one they care about day 2 limbs half as much as day 1 limbs,

day 3 limbs 1 quarter as much  as day 1 limbs, and so on.

A delta of 0 means that they don't care  about their future limbs at all,

so they'll repeat their initial choice of mutual sacrifice endlessly.

But as delta approaches 1,  they'll do anything possible

to avoid the pain of infinite triple limb  consumption,

which means they'll choose to spare each other.

At some point in between they could go either way.

by writing the infinite series  that represents each strategy,

setting them equal to each other, and solving for delta.

That yields 1/3, meaning that as long as Crispy and Chewy care about tomorrow

it's optimal for them  to spare and cooperate forever.

This analysis isn't unique to cookies and wizards;

we see it play out in real-life situations

like trade negotiations and international politics.

Rational leaders must assume  that the decisions they make today

will impact those of their adversaries  tomorrow.

Selfishness may win out in the short-term, but with the proper incentives,

peaceful cooperation is not only possible, but demonstrably and mathematically ideal.

As for the gingerbread men,  their eternity may be pretty crumby,

their friendship will never  again be half-baked.