Vsauce!
Kevin here.
I’ll sell you this 100 dollar bill for 1 dollar.
Seriously, that’s a pretty amazing deal for you, right?
It’s a free 99 bucks!
So?
Whaddya say?
Do we have a deal?
Great!
Here ya go...
What was that?
Huh?
Oh, it sounds like your friend Billy will give me 5 bucks for my 100 dollar bill.
And that’s a better deal for me.
So...
Billy, you've got yourself a...
Hey!
Aren't you gonna outbid him?
If you bid 10 bucks for my 100 dollar bill you can still win a 90 dollar profit.
So… aren’t you gonna do that?
Of course you are!
Why wouldn’t you?
It’s the rational thing to do.
But there is a catch.
Before we get to that….the concept of buying money with money made me wonder how much money
it costs to buy money?
According to the 2018 Federal Reserve currency budget, it costs 5.6 cents to print a dollar
bill but 13.2 cents for a hundred note.
It costs 136% more because it has fancier anti-counterfeiting technologies like this
blue 3D ribbon thing.
You can buy 240 authentic Monopoly money bills, the most printed currency in the world, for
$6.78 or about 2.8 cents per note.
And a $10,000 stack of the prop hundreds used in movies runs $25 bucks.
Or 0.25 cents per fake one hundred dollar bill.
But I will sell this real hundred dollar bill at auction to the highest bidder.
Between you and your friend.
The catch is that not only do I get the winning bid obviously, because the winner is buying
my bill, but the second-highest bidder also has to pay me their losing bid.
So you definitely don’t want to lose or else you’re just throwing away your money
for nothing.
So where did we leave off?
You bid 10 bucks and your friend Billy bid 5.
If he drops out now, that means you win!
You pay 10 bucks for my 100 dollar bill, netting yourself a 90 dollar profit and your friend
pays me his losing bid of 5 bucks.
But he’s not gonna drop out of the game because he can just outbid you with $20 bucks.
And if you drop out that’s the easiest $80 bucks that Billy has ever made.
Hopefully.
So you outbid him at $30 bucks.
He goes to $40.
You go to $50 and I’m about to be very, very happy.
By the way, if anyone has already figured out the mess that’s about to unfold here
-- I’ll explain how you figured that out in just a bit.
Alright, Billy bids $60 for my $100 dollar bill and I’ve officially just made a profit.
As long as the winning bid and the losing bid combine to be more than $100 bucks - I
win.
So if the winning bid is $60 dollars and the losing bid is $50 - I get paid $110 bucks
for my $100 bill.
A cool $10 dollar profit for me and a gain of $40 for the winner.
Here’s the thing.
Even at $99.99, whoever wins is still coming out ahead.
Even if you’re just getting a free penny.
And the higher the bidding goes, the more money the losing bidder will lose.
So you both keep bidding $70.
$80.
$90.
When you first started this game, $100 for a buck sounded awesome.
But $100 for $90… not as awesome.
Still totally worth it, though.
So we keep going.
Billy doesn’t want to lose his $80 bucks for no reason so he bids $100 and we’ve
officially reached dollar equilibrium.
Billy just agreed to pay $100 dollars for $100 dollars.
The profit incentive to keep bidding is now gone.
But minimizing the loss compels you to bid $110 dollars because that way you’re only
overpaying $10 dollars for my $100 dollar bill and you’re not losing your $90 bid.
But Billy doesn’t want to lose $100 dollars so he bids $120.
At this point you’re locked in an endlessly increasing contest to see who can pay more
money for my one hundred dollar bill.
All the while telling yourself that you’re doing the right thing, because based on your
previous bid, you are.
In a 1976 volume of the journal, “Organizational Behavior and Human Performance,” Barry M.
Staw called this the ‘escalation of commitment.’
You’re already in, you know the rules and you might as well keep going, because you
don’t want to lose.
So the bidding grows.
$130.
$150.
$1,000 dollars for my $100 bill.
Once we passed the $100 dollar bidding threshold, I’m the only one who can win this game.
Because you two can’t -- ever.
Before bidding hit $100 bucks one of you could have won the auction and made a profit, that’s
why you kept bidding.
That’s why you got into this game in the first place.
But as long as everyone playing makes a rational decision based on their prior action, the
bidding reaches a point where it’s impossible to come out ahead of where you started.
It becomes impossible for you to actually win.
When Yale economist Martin Shubik published “The Dollar Auction game: A paradox in noncooperative
behavior and escalation,” he wanted to demonstrate the paradox of something with a defined value
like a dollar bill selling for more than that amount due to perfectly rational behavior.
He conducted his game at cocktail parties with large groups of people when quote, “spirits
are high and the propensity to calculate does not settle in until two or more bids have
been made.”
He was using $1 bills, and he said that it wasn’t uncommon for bidding to reach $3
to $5.
3 to 5 times the amount of his buck.
Once Shubik’s auction begins, it’s almost guaranteed to ruin everyone but the auctioneer.
And that was his point: some games you can’t win because escalation based on rational decision-making
drives you to an irrational result.
For those who figured out what was going on before the bidding war began -- you used backward
induction.
A method of reasoning in which you start at the end of a scenario and determine which
choices along the way are optimal.
By the time you worked your way back to the beginning, you could tell that even if you
rationally did the right thing -- you kept outbidding Billy based on the commitment to
your previous bid -- this was going to end badly.
For both of you.
In game theory, it’s a no-win situation -- no matter what choices you make, you’ll
never gain from them.
Shubik’s lesson here is clear: beware of escalation, and sometimes the only way to
win a game is to not play it.
And as always - thanks for watching.
Uhh..oooh I'm getting a little squirrel-y now about what I've done and what I haven't
done.
So this was zero.
Um, so I just missed out on one.
Now.
At one.
Oh no.
Um.
Can we just cut?
I need to think.