Nash Equilibriums // How to use Game Theory to render your opponents indifferent

[@airsquid8532]

I love these game theory math videos. I think that there’s enough information about the topic to make an entire game theory college course.

[@DrTrefor]

That’s totally right! My plan is about ten vids for now, which corresponds to what I do in my math modelling course, about a three week unit.

[@AvoniasStratigis]

@@DrTrefor While I was doing my undergrad in Physics, I took a course on Operations Research and came across Game Theory in the textbook I had. It was very math heavy and used Simplex method for introduction. I always wanted to learn Game Theory, at least get an overall intuition before I moved onto a math heavy treatment. These videos are really nice, gives a good working overview :) . Please do make a full fledged course!

[@Bunnokazooie]

You are very engaging. I finally understand what Nash Equilibria are!

[@dauletmukhamedyarov7740]

you are a very good professor and explain concepts very good. thank you so very much

[@CocoaMilka]

Found your channel when I was taking calc III last semester, I have stuck around since and have really been enjoying your game theory series! :D

[@DrTrefor]

Cool! Glad you have been enjoying:)

[@sdsa007]

I got the Trefor discount on Brilliant! Thanks!

[@DrTrefor]

Awesome! Thank you!

[@miguelavalos1316]

Your channel is awesome!

[@DrTrefor]

Thank you so much!

[@mistertheguy3073]

I absolutely love your content! Small point of feedback: your mic overpeaks sometimes, when you talk a bit louder, which makes the audio quality suffer. Investing in a better mic would have great returns!

[@luukderuijter1332]

I'd Suggest using a compressor or limiter, as he tends to almost yell when he gets excited

[@joydeepburman5269]

Great explanation !

[@aashsyed1277]

gr8 video

[@timandersen8030]

Thank you Dr. Bazett. Can Game Theory be used to describe morality and ethics? If not, how can math best describe it?

[@DrTrefor]

Absolutely it can help inform this, my students did a class project related to e to ethics in medicine and game theory last year!

[@luukderuijter1332]

You can even expand this to evolution and population behavior as a whole

[@ricardobautista-garcia8492]

I need this if I return to goalkeeping.

[@ricardobautista-garcia8492]

Also, you are in Canada? Perhaps you mentioned this before but it is nice to hear. If only you were in NB.

[@DrTrefor]

I am! Victoria:)

[@ricardobautista-garcia8492]

@@DrTrefor Ah on the other side. Hopefully all is well over there.

[@pranshkhubchandani8102]

Too op

[@azhaanali1109]

great video

[@bscutajar]

If a nash equilibrium always exists, then what is the nash equilibrium for the goalie example if you do NOT consider the mixed strategy?

[@DrTrefor]

There is no “pure” mash equilibrium here. The theorem is only for existence of mixed equilibria

[@CristalMediumBlue]

@@DrTrefor In 5:40 you said that there is always at least one Nash equilibrium if the game has a finite amount of pure strategies. Did you mean "mixed" instead of "pure" strategies?

[@Sahilsah02]

Why less views this is not fair

[@coolgarrett17]

Apparently youtube algorithms are a dominated strategy

[@JoshuaGAlbert]

In your economics example, if you change the -50 to +50 then you get x=2 which is not a valid probability. Can you comment and perhaps address what constraints your require the reward matrix to satisfy?

[@Joaking91]

It means that you cant force indifference: no matter what you do, the competition will always benefit more by choosing to enter. It wins either 50 or 100 vs always 0 if they choose not to.

[@ronniec8805]

fat better than my lecturer. Thanks!

[@DrTrefor]

Sorry to hear that, but glad you enjoyed!

[@Sahilsah02]

❤️❤️❤️❤️

[@unknowninfinium4353]

Is there a way to win with game theory? Not getting equilibrium but actually winning.

[@user-or7ji5hv8y]

Is there a Discord channel, where we can all share and ask questions to each other? Just an idea.

[@DrTrefor]

Not yet but I’ve gotten a few requests for this so maybe I’ll do one at some point!

[@aashsyed1277]

@@DrTrefor ok!

[@NickKravitz]

Several classical games use this principle; notably poker. There's an old saying in poker; if you make a play 100% of the time you are playing 100% wrong.

[@lennykoss8777]

💗

[@配達員です-x3u]

すげー

[@falconhawker]

What about running to the ball fast, but hesitatng an instant . the goalie jumps , then kicking ?

[@aashsyed1277]

this video is not in the game theory playlist!

[@DrTrefor]

What would I do without you?

[@aashsyed1277]

@@DrTrefor:)

[@benjaminshropshire2900]

Actually the best strategy is for the companies to collude, divide up the states and agree to not compete ... assuming they can avoid getting noticed by the FTC.

[@tmcche7881]

Canadians can't play soccer. The ice is too slippery. ps. How does the Nash equilibrium thm consider the quality of execution in a real world game?

[@DrTrefor]

lol:D Typically what we do (and will see a bit of this later on) is to think of this probabilistically. For instance, we say something like that "when you kick to the opposite side of the goalie you score 75% of the time, and 25% of the time you are wide/hit the post/etc". These elements can then be incorporated into the model.

[@mathadventuress]

render them indifferent? great so they no longer care about the game :P

[@DrTrefor]

haha then we would definitely win!

[@luukderuijter1332]

I like the video, but i could do without the yelling