How Decision Making is Actually Science: Game Theory Explained

With up to ten years in prison at stake, will Wanda rat Fred out? Welcome to game theory: looking at human interactions through the lens of mathematics. Want to learn more? Join Hank Green and play along in this fun new episode of SciShow!
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[MindYourDecisions]

There is a big mistake in this video. The definition of "Nash equilibrium" in the video is actually the definition for a strictly dominant strategy: "A player in a game has found A STRICTLY DOMINANT STRATEGY when they make the choice that leaves them better off no matter what their opponents decide to do.”

In the prisoner's dilemma, each player has a strictly dominant strategy to confess--it's better NO MATTER what others do.

A Nash equilibrium, by contrast, is when each player has a strategy that is better GIVEN what others are doing. Each person is doing the best to outguess others, and mutually each person is playing a best response.

Here's an example to illustrate the difference. Do you drive on the left side of the road or the right? There is no choice better for you "no matter" what others do. Your best choice is to match what others do: you drive on the left if others do, and you drive on the right if others do too. This game does not permit a strictly dominant strategy. But there are two Nash equilibria--when everyone drives on the left, or everyone drives on the right.

Very few games have strictly dominant strategies. In contrast, every game* has a Nash equilibrium (*under certain conditions) Nash proved the existence of the equilibrium in his doctoral thesis at Princeton, and that is work for which he was recognized with a Nobel Prize and is the subject of the book/movie "A Beautiful Mind."

I mostly liked this video and the Shapley value example is good. But the definition of the Nash equilibrium is a big error--perhaps include a note or annotation?

[kjs]

Watching this in 2020.
"Did you interact with anyone today?"
No. No I did not.

[matthughes]

"Did you interact with anyone today?" ha... ha...

[AwokenEntertainment]

Love how you break-down what is common sense to most.. it really forces me to understand why I think a certain way in situations where I'd normally think automatically

[razvan]

HELLO INTERNET; WELCOME TO GAME THEORY!

[wyattcastle]

If I were a betting man I'd say that there is at least one comment in here referencing Matthew Patrick.

[surindervirdee]

This is probably one of the more concise, bitesize videos on understanding game theory, very helpful.

[coastermania]

that example reminds me of the game show Friend or Foe. two players have acquired a certain amount of money based on their performance in the game. Then at the end they make a secret decision. If they both choose the Friend option, then they split the winnings 50/50. If one chooses Friend and the other chooses Foe, then the person who chose Foe gets all the winnings and the other person leaves with nothing. If both people choose Foe, they both leave with nothing

[socratz]

1. "pioneered by John Nash"!

John von Neumann is the father of game theory! John Nash found the equilibrium exist in a much more general class of games, but his contributions are less significant than von Neumann's.

2. (4:26) "no matter what everyone else decides to do"

The whole purpose of studying game theory is that others actions affect your outcomes, and perhaps your optimal actions. You should say: taking into account what everyone else decides to do. The above condition doesn't make sense in a game theory context.

[Fzzt]

"Did you interact with anyone today?"
I don't like your tone there hank. Feels a little personal.

[jinjeredge]

5:55 "DUMMY PLAYERS HAVE ZERO VALUE"

*Luigi* would like to speak with you.

[maxr]

Ive be running this in my head to make situations work for me without even realising it was a thing.

[morgengabe]

As someone who's been stuck watching intro game theory videos for about 5 years, this is the best one I've seen to date. Very clear and concise description, Sci.

[callumleask]

I can't be the only one expecting a matpat crossover

[trevorfielding]

I'm glad you guys went with SciShow Psych. I've been loving those vids!

[robertschlesinger]

Excellent video on the basics of Game Theory. My 17 year old learned a lot from it. It may also be worth mentioning that Game Theory is put to good use by economists, military strategists, and policy strategists. Differential Games are more difficult to axiomatixe and compute, but often more accurately reflect real world situations. Military strategists generally use Differential Game Theory, as situations are often continuously changing.

[parsont.]

Von Neumann and Morgenstern pioneered/created Game Theory in the 1920s-1940s. Nash made important contributions.

[bitflipped]

the prisoner dilemma made me remember a scene from The Dark Knight, that ship scene. Just sharin

[johnnydoe]

That's just a theory, a GAME THEORY! Thanks for watching!

[DsLink]

Hank, you didn't end the video right. See according to game theory your ending was supposed to be.

"And remember its just Science* Thanks for *Learning*