A Game You Can Never Win

A Game You Can Never Win


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!
Hey!
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.

99 Comments on “A Game You Can Never Win”

  1. HI THERE, YOU. I took the summer off to write a book. I was able to get 10 chapters finished, looked at the calendar, and realized it was time to get back to you. So I'm back. Hello. I will work on the book during weekends until it's finished. For now, expect more videos, more frequently. And as always… thanks for commenting.

  2. I don’t get why the one who is not getting the 100$ in the end still has to pay what he was bidding. At an auction only the highest bid has to pay and gets what they were bidding for… can someone explain?

  3. In fact, you can win if you agree to cooperate :
    You pay 1$, Billy gave you 0,5$ and you share the 100$.

    Cooperation is the solution

  4. Sure, I’ll take your $100 for $1!
    *Billy bids*
    Welp, that’s a waste of a Dollar
    “Aren’t you going to outbid him?”
    No!

  5. you're supposed to bid $99 the first time cause no one else would want to bid… unless they have something against you lol

  6. This game is also displayed in an anime, it was really interesting seeing how it ended.

    Kakegurui XX
    Final Episode
    Game: Hundred Votes Auction

  7. I would buy that for one dollar, and my friend would give u 5 dollars, and I quit! U take my 1 dollar and me and my friend we go with your 100 dollars

  8. Both of us bid 100 dollars, meaning you gotta pay us both a 100 dollars which means you make no profit and we make no profit

  9. I think if you are forced to play this game then the best move is to instantly bet 100$ so your friend has no incentive to outbid you. This way you limit your potentially infinite losses to the minimum of 0$.

  10. but i am smart and do not care what my friends pay, just wait till he doesnt say any higher numbers

  11. What if you're in competition with Billy beyond just this auction? If Billy has more money than you have, then he has more buying power than you have. Being ten dollars in debt when your rivals are one-hundred dollars in debt is a more advantageous position than being flat broke but debt free while Billy is a hundred dollars richer.

    Even not playing is a losing strategy in the long run.

  12. Today the game is called : "How much =$= do I put into the car to get it fixed again"
    Cause you don't want to lose the $4,500 you spend last week for nothing, do you? 😀

  13. Fun way to win that game
    If there’s multiple rounds just bid 101 off the bat until the other players realize that you don’t care how much you loose then only bid one dollar they’ll most likely not outbid you since they know you could bid 101 and so you have successfully been able to make a profit

  14. So as a game it makes sense. But in the real world this won’t work out for you. Because this is how bidding works: if person 1 bids out person 2, person 2 doesn’t have to pay, because he doesn’t get the $100.

    At best, you the seller have no gain. Because if person 1 is paying $99.99 and person two bet $99.99 you would only get 99.99, not $200.

    Only works if you explain the game under your rules. But no one is dumb enough to play it that way. They may even make a deal with each other to lowball you and then take the profits and split it.

    If I have messed up a point, please reply, as I do not mean to be hostile, I just do not understand the point of this video…

  15. You don't pay losing bids in real auctions, this is a thought expriment designed by Martin Shubik, it's rather application of war of attrition into a game. So ye this never happens.

  16. There is a way to win. Just be first and bid 99$, the other guy will not bid 100$ for 100$ since he will not make any profit. So he will quit and you win 1$ profit.

  17. what if i said to bill to he stop bidding at 2 cents…the we would share the profits? 49.99 for bill and 49.98 for me

  18. "Hey billy, imma bid 5.02 dollars, and you'll let me win. I will then give you 49.99 and keep 44.99 dollars and we both end up with a profit of 49.99 dollars"

  19. Billy: "I bid one dollar"

    Me a extremely competitive person : "I bid you my kids , my house , my access card to the white house and my dog"

  20. Or I could team up with Billy. I'll bid 1 dollar and he'll bid 2 dollar and then we split it and let Billy have a dollar more lol

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