GTO-2-03: Computing Mixed-Strategy Nash Equilibria

[@lherath8658]

Thank you from the bottom of my heart!! It's not a complicated thing, I don't understand why professors can't just go over it once properly. I was so confused until I found this video. Hope the best of best to you!

[@perpetualesinamdzudzor6500]

😪 true dear

[@amirkhan355]

I have a strong background in math, and these videos are by far the best I've found online that explain things extremely clearly. Thank you!

[@zhilangzhong7871]

Thank you so much, spending a few minutes here is much more worth listening to my lecturer...

[@PB-cb7ht]

great video. I'm a second year economics undergrad and still find stuff like this useful aha

[@101dostoyevsky]

Thank you very much. I'm finally getting Mixed Strategies. God bless.

[@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.

[@LarryP248]

I'm riveted by this content. A book I read with kindred insights was the impetus for major life changes. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell

[@cherrypoo9742]

Wow thanks a million! Definitely a new subby! I like your teaching style it’s very clear and detailed please don’t change this style and can you please make a video on “Auctions”. I really need you to show me the whole concept behind it just like you did with this mixed strategy, that was genius!

[@Olav3D]

Thanks! I finally understand the calculations :)

[@emiliaborko7016]

Thank you so much ! 'm so glad I found this channel

[@ossamazaiter3302]

Excellent explanations, it would be great if we can have more realistic examples that can be used in management decisions.👍

[@maggielin8664]

Dear Prof. Leyton-Brown, in the battle of sexes the expected utility for both is 2/3, it is even worse than the passive case for each.

[@anabelleginez1822]

If we find a negative probability for player 1 and a positive probability for player 2, is it an equilibrium in mixed strategies?

[@SUPER7X]

Helpful. Thank you!

[@sdyz2161]

this is actually really helpful and clear. thanks :)

[@maryammusallam9032]

thank you so much, so clear.

[@Saeed-jf8lg]

so what about a 3x3 bimatrix game? can't find this anywhere. meaning, with the same process. using probabilities

[@kzoo_]

hello, im not sure if you still need help with this, but the method to compute mixed nash remains largely the same: assign probabilities p1, p2, and 1-p1-p2 to actions.

[@xinruiyang6059]

Thank you ! It is really helpful!

[@ojo7303]

4:02, but why does p2 care about making p1 indifferent? isn't p2 a self interested individual, so why does p1's payoffs matter?

[@MightySwifter]

finally understand this. thanks!

[@AsakuraYukiko]

Test tomorrow, I got it.

[@spooie1350]

can there be only 1 mixed strategies?

[@Boristien405]

Nah there can be multiple. If it's symmetric and 2x2 then I think there's just one mixed NE though.

[@mawutjokfilms]

thanks

[@iremlergun]

Awesome!

[@meditationwithtyler]

I only have a background in Algebra. At 5:24, I don't know how to solve the equation. To me it looks like 2p = 1(-1p), which becomes 1p = 1..

[@thanhminhcao3356]

2p=1(1-p) implies 2p=1-p hence 3p =1. P=1/3

[@ShinobiStriker]

@@thanhminhcao3356 This still doesn't make that much sense to me

[@NoName-kr3se]

no comprehend

[@serinacat4781]

thanks very clear

[@HangNguyen-wu3fs]

what do you mean by indifference?

[@sayaks12]

panbee hằng the way I interpret it is that it doesn't matter to me what I choose, I'd get just as much expected utility from each option. like say I had an option of getting $10, or flipping a coin and getting $20 if it's heads. in the first option I'd expect to get $10, in the second I'd expect to get $20 half of the time, so I expect $10 om average. so I'm indifferent, it doesn't matter which I choose cause I'd expect to get $10 either way on average.

[@HangNguyen-wu3fs]

Thank you. The wording was weird in the lecture :)

[@thanhminhcao3356]

Equal utility

[@jillianyip4098]

how was p & 1-p derived?

[@stapler1636]

Four years later, but the probabilities must sum to 1. So (probability of choosing F) for player 2 is (1- (probability of choosing B)). Letting probability of choosing B be symbolized as p, we have probability of choosing F to be (1-p).

[@FG-fc1yz]

3:59