Game Theory 101 (#7): Mixed Strategy Nash Equilibrium and Matching Pennies

[@kaanbursa7626]

I got 9/100 from the exam thanks

[@Gametheory101]

Kaan Bursa I sincerely hope that was 90 or 99 out of 100 and not 9!

[@BlademanZX]

+William Spaniel or 9/10 :P Though I suppose that's the same as 90/100.

[@batman9937]

why did you pin it lol

[@Blizzardsnewman]

@@batman9937 he's into memes

[@ryunderstands8602]

@@batman9937 trust bro homie is nerfing his own channel

[@alexanderharding2221]

I'm going to fail a Game Theory exam tomorrow. Thanks to your videos, I'm going to fail marginally less embarrassingly. Thank you.

[@alexanderharding2221]

UPDATE: I ACTUALLY PASSED.

[@graceh.9015]

@@alexanderharding2221 good work !

[@alexanderharding2221]

@@graceh.9015 late thank you 🙏

[@shafiakhtar4360]

I am not not going to fail so watching this video before 2 months from exam.😂.

[@Kalernor]

@@alexanderharding2221 LET'S GOOOO. (Belated) Congrats!

[@Gametheory101]

You can calculate best responses like that, but keep in mind that we mostly care about equilibrium. So you really need correspondences to get that to work.

[@abdoulayesaadou4448]

Thanks a lot. I understood how to compute the probabilities in the case of two players. What if we had 4 players instead? Suppose player 1 & 2 maintain their strategies while players 3 & 4 adopt player 2's strategies.

[@thomasmatthews80]

Loving these in 2024. Book great too. 🎉

[@Rachel-jx1xs]

Hi William, I didn't quite get this video so hope you don't mind clarifying:) For a mixed strategy Nash Equilibria to happen: -The outcome must be zero-sum -There is no best dominated strategy -There is no pure strategy Nash strategy Equilibria And the way it works is: -Players simply randomly choose(?) Is my understanding correct?

[@Gametheory101]

+alittlepenny saidhi I have some caveats. There are MSNE in non-zero sum games. There are MSNE when there are also PSNE. And you can have MSNE when a player has a single dominant strategy. You'll see examples of all of these later in the course.

[@soapbxprod]

That's the absurd point of Nash's mixed strategy. There is actually no strategy at all.

[@Mashayach7]

Woooow, I was wondering what the poison game in The Princess Bride would look like in terms of game theory and came across a Cornell University blog that explained it like this. Now I actually have a better grasp of what they were getting at.

[@zumiao234]

Thank you！Got to attend an exam the day after tomorrow and you saved me!

[@giorgiocilano4483]

Hi William, is it possible to have the text of what you explain? because I don’t speak English very well and I would like to fully understand these topics on game theory by watching your videos. Thank you very much

[@Gametheory101]

The textbook is basically a written version of these lectures with a lot more examples.

[@mage1over137]

actually now that think about it the input vector would could be any unit vector, and you could vary it until you find the maxs. So just ignore my last sentence.

[@RyanSlama]

I would just think insane things until the mind reader left my thoughts to myself.

[@dgk2789]

Pause: suppose you were against minder reader, yes.. I will just flip the coin !

[@mage1over137]

if your strategy is represented by a vector which each element is the weight of that strategy. Multiply by the payoff matrix than dot with the other strategy vector, this would be a map from a vector space to the reals. You can than find local maximum. Also this would be on a grid not plane, though generalization might be possible.

[@Gametheory101]

Can you describe that in a more detailed way?

[@sebastianhjarndal9110]

i get what a Pure strategy Nash-e......., is but when you just say pure strategy what do u mean?

[@joypalit6408]

Hi sir! U have mentioned that if we flip the coin then we will get Nash equilibrium. So, in penalty kicks what is the analogue of "flipping the coin"?

[@Gametheory101]

Here's an example: kzbin.info/www/bejne/jXOmiKqKfLKBmsU

[@joypalit6408]

@@Gametheory101 thanks

[@ARP2wefightforyou]

But there was no Nash equilibrium in the original game, i.e. the one without mind readers.

[@kkTeaz]

Both flip

[@spike9985]

Im convinced you're Ben from Parks and Rec.

[@Gametheory101]

Funny you should mention that, my next video is about optimal strategies in the Cones of Dunshire.

[@ngahngako8739]

Pleas will like to nkow if the always exist a nash equilinrium in a mixed strategies

[@williameuerle3460]

diametrically opposed.......foes

[@mage1over137]

Can we think of mix stagey as a vector, and the payoff matrix as a two form. Then optimize using finding basically the local maximum?

[@harveyspecter3361]

Yes you can!

[@thomasmatthews80]

This is where the application to poker GTO comes in …

[@sami-samim]

Can we apply mixed strategies to pure nash equilibrium? (For a game where it has a pure nash equilibrium).

[@Gametheory101]

+Sami Samim Yes. Keep watching. There are some examples upcoming.

[@sami-samim]

Many thanks.

[@harveyspecter3361]

Pure strategies are basically mixed strategies where one player has probability of 1 in one (pure) row or column.

[@divyanshupathak2327]

hey William I am studying game theory from Martin j Osborne book I find problems in that book difficult . can you help me ?.

[@ronitlenka9205]

Read Gibbons.

[@area___]

how does either "know" what the other player will choose?

[@ViciousRanger]

At 4:30, why do you say "At best", wouldn't it be "On average"?

[@dannymunoz8027]

Good work

[@normanhofer8965]

really really good! 'n nice speed!

[@bivasbisht1244]

explanation is awesome , but dude you speak really fast

[@Verbti]

So how can I use what I learn here to say every day decision making. I'm having a hard time devising these boxes.Solving them though seems doable.

[@Finition1999]

thanksss

[@jamessheng1107]

Well, what i am thinking is that if you are facing a mind reader who knows what exact you are thinking, and you know that he is a mind reader who knows what you are thinking. Then you can directly response to his behaviour since you can predict his behaviour based on the assumption that he knows your behaviour. Take an example, assume you will pick head, he knows you will pick head so he will pick tail. Since you know he can read your mind so that you know he will pick tail. Then you will also pick tail to response. Take action before the mind reader read your mind again so that he realise you will pick a tail since you know that he will pick a tail response for your first mind, you can win the game.....

[@David-lr4mh]

That's called levels of reasoning

[@SwissSareth]

This assumes that the mind reader isn't constantly reading your thoughts.

[@ivoriankoua3916]

But......he already knows that....so you're better flipping.

[@soapbxprod]

This argument is logically absurd. A mind reader would know that you were going to flip the coin, yes?

[@Silamoth]

Yes, but what good would knowing that do the mind reader? The mind reader still wouldn't know what it would land on.

[@soapbxprod]

That's the absurd point of Nash's mixed strategy. There is actually no strategy at all.

[@JJ-fb2lp]

mind reader cannot know which side of the coin it would land on that is why we need mixed strategy....

[@harveyspecter3361]

Uhm, the mind reader cannot control the outcome of the coin ending up being heads or tails. In this case, it is useless to know what the other player will play.