On "Billions" and Game Theory

The show "Billions" is a guilty pleasure of mine, I don't care for much TV but this show has managed to suck me in. After watching the

throughout the show I've become intrigued with Game Theory and how little I know of it.

Do you guys use Game Theory in your day to day, study it, etc? Also - what are some good books, websites, blogs to learn more on this subject. I recently ordered the book, [Thinking Strategically]

(https://www.amazon.com/Thinking-Strategically-Com…), to learn more.

 
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Interesting topic. You can of course find examples of game theory played out in numerous fields- business, politics, war, etc but I find game theory in sports the most fascinating.

The 2008 Champions League final penalty shoot out displayed game theory in its rawest form. Chelsea discovered that Van de Sar, the United goalkeeper tended to jump in the natural direction of the kicker, for example, if the shooter kicked with his right foot, Van de Sar would jump right. So, they followed the game plan of kicking to the opposite side (the kickers weaker side-left side in this scenario) and Van de Sar as expected dived to the wrong side. This worked for a few goals.

Then it gets interesting.

As Chelsea striker Nicholas Anelka took the pitch for the deciding shot of the game, Van de Sar called him out. “You’re going to put it there, aren’t you? I’m onto you guys and your little plan. Not this time son, not this time,” he yelled, pointing the left corner, on Anelka’s opposite shooting side. Anelka now faced a very interesting decision: should he shoot left to continue with the plan to exploit Van de Sar’s weakness, now that he knew that they knew? Or should he account for this, and go on the right?

In the end, Anelka shot right, and Van de Sar blocked it, winning the game and making history.

 

That's a very interesting example. Maybe I'm missing something, though, but why did Van de Sar call him out? If he had figured out what they were doing and it was reasonable to think they would do it again, he could have said nothing and attempted to block a shot off the kicker's weaker foot.

"Successful investing is anticipating the anticipation of others". - John Maynard Keynes
 

The way I look at it, you want to randomize the direction of your kick or your dive (depending on your role in the situation). Even if Van De Sar figured out where Anelka was going to kick, it was still a 50-50 shot. What Van de Sar did was remove the randomness and "force" Anelka to change the script and kick towards his stronger side. This way, I think it more than a 50-50 shot as there is some certainty that the kick was going towards his stronger side. Now, would most people do what Anelka had done and change the script at the 11th hour just because the plan was busted? That is a topic for another day.

 

game theory is just a fancy way to say winning at life. you're using game theory constantly. just might not be aware of it. which line do i stand in at the grocery line? how do i reply to this text? if i say this, it reveals that i know that. if i say that though, it can yield a different result than if i say this. etc. shit, choosing which book to read next is game theory, your enemy is out there reading too. he's making decisions as well.

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I didn't throw the MS but the comment is a little dismissive. I wouldn't say choosing the right grocery line is game theory, c'mon now.

But I agree game theory is closer to common sense than many game theory dudes would have you believe. I went to a 'quanty' MBA program and at least 20% of my classmates were obsessed with game theory and behavioral stuff. Any time we had a guest speaker on game theory I was like awwww shit there are gonna be some sore wieners after this one.

I think some folks just really want it to matter more than it does because they have fun reading about it and wish it could be their life's work.

 

I'm with you! I think any situation where you have a clear, defined goal you are pursuing is an opportunity to take a step back and assess how it would be useful, particularly if it involves other people (i.e., a promotion, a deal or particular engagement).

 

Structured most of my Economics degree around game theory electives. Find it wildly interesting as well.

I haven't done much structured reading (cover to cover) on it but one of the leading books in the field is "Theory of Games and Economic Behavior". Many of the books you read will be a little bit dry (Depending on how interesting you find the topic).

Some really cool thought exercises are the "Red Hat" problem and the "Blue Eyed Islanders" problem.

BLUE EYED ISLANDER PROBLEM:

A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?

There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

Please don't look up the answer and ruin it for anyone. Also, if you think you have an answer also provide a logical explanation as to how and why it is correct, as best you can. Good luck!

 

I don't know the answer but I'll think about this stream of consciousness. So my first thought is there's nothing special about the number 100 or 99 except maybe to scare you or short circuit your brain imagining a huge crowd. I don't think the prompt answer differs if it's 50 of each, or 20. So maybe I'll try to find the smallest number crowd that makes sense. I also don't like the fact blue and brown start with the same letter, so I'm going to say the guru has brown eyes and the crowd is blue and green so I can use B and G.

If there is 1 guru and 1 crowd member, the guru says blue eyes, the member knows he has blue eyes, he leaves.

If there are 2 crowd members, the guru says blue eyes, now we have to consider three unique possibilities for the two members: BG, GB, and BB (GG is not a possibility since one of them has to be blue). 1. BG. From the first member's perspective, they will see green eyes (at which point they know they have blue eyes and will leave the island that night) 2. GB. From the first member's perspective, they will see the other person has blue eyes. But that doesn't help the first member rule out whether the situation is GB or BB. But the first member knows the second member can see his eyes. If the second member leaves that night, then the first member knows that his own eyes are green since the second member can deduce his own eye color. Actually since the eyes can be any color the first member still doesn't know his eye color, just that it's not blue, so the first member doesn't leave the island. 3. BB. If in (2) the second member stays overnight, that means they are actually thinking they are the "first member" scenario from (2) and are watching the first member to see what they do. If neither leave, that means they both have blue eyes, and they both must leave the island.

If there are three members, four members, etc. that all seems similar to me so the answer is probably the same, so what is the answer for three members? Seems trickier. You could have:

  1. BBB: people stay over one night, see everyone is still here. 1 knows that 2-3 have B, 2 knows that 1-3 have B, 3 knows that 1-2 have B. But nobody knows what color their own eyes are. I think at this point all of them would deduce that they all have the same eye color and leave, as this eye color is blue, because...
  2. GBB / BGB / BBG: If it weren't the above, and for example 1 had green, then 2 with blue eyes not leaving after the first night would mean 3 is looking at 1G 2B, because if 1G 2G then 3 would have left the island having known their eyes are blue since they're the last out.
  3. GGB, or BGG, or GBG all easy as before, the blue person knows it so they leave after the first night when nobody else leaves.

So I don't know whether this is right, can't be bothered to think about 4+ and if anything special about the timing of how many nights (could you deduce everything with for example one night per additional person? Just a guess / intuition since if 1 person, 0 nights, 2 people, 1 night, 3 people, 2 nights). I think eventually all the blue eyed people leave after at most N-1 nights if N is the number of people in the crowd and not counting "leaving at midnight" as an overnight stay. I guess I mean N-1 morning afters.

If I'm right I'll take my park anywhere pass.

Be excellent to each other, and party on, dudes.
 

+1 and definitely agree you are in the running for user of the year.

Depending on the nuance and "day timing" it would be that the blue eyes populace leaves on N or N-1 days, all at the same time as the only way to come to a logical conclusion is to iterate what you and @tryna trade laid out until you hit the Nth person that then realizes the only reason all the other Blue eyed people aren't leaving is because there must be one additional person, which would be themselves. (In this case that "Last person" is actually every single person with blue eyes, all of whom realize this at the same time).

Good job guys, this is definitely one of my favorite thought experiments. Game theory revolves pretty heavily around information asymmetry.

Great clip demonstrating that

 

100 people leave on the 100th night.

Start with the base case that there is one person with blue eyes - they see that no one else on the island has blue eyes and so they leave that night, knowing that the guru must have been talking about them.

Now let's move to the next case where there are 2 people with blue eyes. Each sees one person that has blue eyes (the other) and expects them to leave on the first night, following the logic above. When this doesn't happen, the person deduces that they must also have blue eyes (because they see that no one other than that one other person on the island does, and they must have seen someone else with blue eyes if they didn't leave on the first night), and both people leave on the 2nd night (both people follow the same process).

Etc., etc., 100 people leave on the 100th night.

 

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