During World War I, peace broke out.

It was Christmas 1914 on the Western Front.
Despite strict orders not to chill out with the enemy, British
and German soldiers left their trenches, crossed No Man's Land,
and gathered together to bury their dead, to exchange gifts, to sing.

Meanwhile: it's 2017, the West has been at peace for decades, and
we're less trusting than ever. Fewer and fewer people say they trust their
governments, their media, or even each other. So here's our puzzle:

Why, even in good times, do friends become enemies?
And why, even in bad times, do enemies become friends?

I think game theory can help explain our epidemic of distrust –
and how we can fix it! So, to understand all this...

...let's play a game. →

you
cooperate

you
cheat

they
cooperate

they
cheat

you
↙

other player
↘

THE GAME OF TRUST
You have one choice. In front of you is a machine: if you put a coin in the machine, the other player gets three coins – and vice versa. You both can either choose to COOPERATE (put in coin), or CHEAT (don't put in coin).

Let's say the other player cheats, and doesn't put in a coin.
What should you do?

Exactly! Why let that moocher mooch off of you?

Alas, turning the other cheek just gets you slapped!

If you cooperate & they cheat, you lose a coin while they gain three. (score: -1 vs +3) However, if you both cheat, neither of you gain or lose anything. (score: 0 vs 0) Therefore: you should CHEAT.

But let's say the other player cooperates, and puts in a coin.
What should you do now?

Wow, that's mean... and also the correct answer!

Sure, seems like the right thing to do... or is it?

Because if you both cooperate, you both give up a coin to gain three. (score: +2 vs +2) But if you cheat & they cooperate, you gain three coins at their cost of one. (score: +3 vs -1) Therefore: you "should" still CHEAT.

And that's the dilemma of trust. You'd both be better off trusting each other, but trust leaves you vulnerable. But what happens if we can...

...play more than once? →

Now, let's play for real.
You'll be playing against 5 different opponents, each with their own "personality". With each opponent, you'll play anywhere between 3 to 7 rounds. Can you trust them? Or rather... can they trust you?

Choose your first, real move:

opponent: [X] of [Y]

your total score:

And your total score is...

which is, wow, actually impressively bad.

which, uh, could be worse!

which ain't bad!

which is pretty good!

which is perfect! Congrats you have too much time on your hands.

...i have no idea how you did that.

(the lowest & highest possible scores are 8 and 49, respectively)

So who were these strange characters you just played against?

COPYCAT: Hello! I start with Cooperate, and afterwards, I just copy whatever you did in the last round. Meow

ALWAYS CHEAT: the strong shall eat the weak

ALWAYS COOPERATE: Let's be best friends! <3

GRUDGER: Listen, pardner. I'll start cooperatin', and keep cooperation', but if y'all ever cheat me, I'LL CHEAT YOU BACK 'TIL THE END OF TARNATION.

DETECTIVE: First: I analyze you. I start: Cooperate, Cheat, Cooperate, Cooperate. If you cheat back, I'll act like Copycat. If you never cheat back, I'll act like Always Cheat, to exploit you. Elementary, my dear Watson.

Now, what if these characters were to play...

...against each other? →

It's tournament time! Each character will now play against every other character: that's 10 paired matches, and 10 rounds per match.

Who do you think will get the highest total score? Think carefully about it, and then
PLACE YOUR BETS:

Alright, you placed your bet on [CHAR]! Let's go through the matches one by one, and see how the tournament plays out...

first match →

next match →

Match #[N]: [A] vs [B]

Rounds:

Total Scores: [A] vs [B]

Oh, by the way...

[trench live & let live stuff]

Anyway -- and the winner is...

(drumroll please...) →

COPYCAT!

Congrats, you placed your bet on the right horse.

(Sorry, [CHAR].)

Copycat goes by many names. The Golden Rule, reciprocal altruism, tit for tat, or... live and let live. That's why "peace" could emerge in the trenches of World War I: when you're forced to play the same game with the same specific people (not just the same generic "enemy") over and over again -- Copycat doesn't just win the battle, it wins the war.

But if things change a lot when you play multiple rounds of the same game, what if we play...

...multiple tournaments? →

Now, let's let our population of players evolve over time. It's a 3-step dance:

1. PLAY A TOURNAMENT
Let them all play against each other, and tally up their scores.

2. ELIMINATE LOSERS
Get rid of the 5 worst players. (if there's a tie, pick randomly between them)

3. REPRODUCE WINNERS
Clone the 5 best players. (if there's a tie, pick randomly between them)

...and REPEAT, for as long as you'd like. Note: you don't have to wait for people to literally die & reproduce for culture to evolve -- all that's needed is that "unsuccessful" behaviors go away, and "successful" behaviors are imitated. So now...

...let's see this in action. →

Say we start with the following population of players: 15 Always Cooperates, 5 Always Cheats, and 5 Copycats. (We'll ignore Grudger & Detective for now)

We're going to do the tournament-eliminate-reproduce dance a dozen times or so. Let's make another bet! Who do you think will win the first tournament?

Makes sense, Always Cooperate outnumbers everyone else right now...

Makes sense, Always Cheat has a lot of Always Cooperates to exploit...

Makes sense, Copycat won the tournament last time, why not again?...

Let's see if you're correct:

1) play tournament

2) eliminate bottom 5

3) reproduce top 5

Alas, Always Cooperate got eaten up by Always Cheat, whose numbers have now increased by 5.

Sadly, you were correct! The Always Cheaters won this time, and their numbers increased by 5.

Alas, Copycat did not win – but at least they didn't do as bad as Always Cooperate, who got eaten up by Always Cheat, whose numbers have now increased by 5.

But let's try a few more rounds of this...

Always Cheat is still growing, at the expense of Always Cooperate...

And now, all the Always Cooperates are dead. But, wait...

That's right: the Always Cheats became a victim of their own success! They exploited the naive Always Cooperaters, but once they ran out of them, they had to face the Copycats: who are nice, but not naive.

By simply copying the other player's moves, Copycats can play nice with each other, while Always Cheats just cheat themselves. Not only that, but it also means Copycat can give Always Cheat a taste of their own medicine.

And so, as a result...

...Copycat inherits the earth.

So, although your bet was off -- the nice-but-naive Always Cooperaters were doomed from the start -- in the end, a smart form of niceness prevailed, and the Always Cheaters were squashed.

So, in the short run you were right - Always Cheat won the first few rounds, but in the end, its exploitativeness was its downfall.

So, in the long run, you were right - Copycat wins! Always Cheat may have won in the short run, but its exploitativeness was its downfall.

This reminds me of a quote:

"We are punished by our sins, not for them."
~ Elbert Hubbard

(oh, and by the way...)

(...this result is similar even if we put Grudger & Detective back in:)

start the evolution process!

stop the evolution process

(Note: occasionally, a few Grudgers may stick around, because when all players except Grudger & Copycat are eliminated, the two tie.)

So, it seems the math of game theory is telling us something: that Copycat's philosophy, "Do unto others as you would have them do unto you", may be not just a moral truth, but also a mathematical truth. However...

...there's a problem: →

There are jerks. Look around.

If Copycat is the strategy in this repeated game of trust that's so powerful -- that even soldiers in the trenches of World War I independently "evolved" a similar strategy -- why, then, are there so many un-trusting, un-trustworthy people around?

A clue's in that sentence itself. "In this repeated game of trust." So far we've only talked about change in the players: what about a change in the game? What could lead to...

...the evolution of distrust?

Start off with this distribution of players:

The payoffs in a one-on-one game are:

reset payoffs

Play [N] rounds per one-on-one game

Play [N] round per one-on-one game

After each tournament, eliminate the bottom [N] players & reproduce the top [N] players

After each tournament, eliminate the bottom [N] player & reproduce the top [N] player

In each round of a one-on-one game, there's a [N]% chance a player makes a mistake

...once you're done playing around in Sandbox Mode, click:

blah blah blah blah blah blah blah blah
blah blah blah blah blah blah blah blah
blah blah blah blah blah blah blah blah
blah blah blah blah blah blah blah blah

Copycat

copycat

Copycat

Always Cheat

cheater

All Cheat

Always Cooperate

cooperater

All Cooperate

Grudger

grudger

Grudger

Detective

detective

Detective

Copykitten

copykitten

Simpleton

simpleton

Lol So Random

random

cooperate

cheat

play

stop

step

reset

population

payoffs

rules

0. Introduction

1. One Game

2. Repeated Game

3. One Tournament

4. Repeated Tournament

5. Making Mistaeks

6. Sandbox Mode

7. Conclusion

Credits