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!
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.
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
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.
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!
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.
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).
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!
😪 true dear
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!
Thank you so much, spending a few minutes here is much more worth listening to my lecturer...
great video. I'm a second year economics undergrad and still find stuff like this useful aha
Thank you very much. I'm finally getting Mixed Strategies. God bless.
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.
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
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.
If we find a negative probability for player 1 and a positive probability for player 2, is it an equilibrium in mixed strategies?
Thanks! I finally understand the calculations :)
Helpful. Thank you!
so what about a 3x3 bimatrix game? can't find this anywhere. meaning, with the same process. using probabilities
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.
Thank you so much ! 'm so glad I found this channel
Excellent explanations, it would be great if we can have more realistic examples that can be used in management decisions.👍
this is actually really helpful and clear. thanks :)
thank you so much, so clear.
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?
can there be only 1 mixed strategies?
Nah there can be multiple. If it's symmetric and 2x2 then I think there's just one mixed NE though.
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!
no comprehend
Test tomorrow, I got it.
Thank you ! It is really helpful!
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..
2p=1(1-p) implies 2p=1-p hence 3p =1. P=1/3
@@thanhminhcao3356 This still doesn't make that much sense to me
finally understand this. thanks!
what do you mean by indifference?
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.
Thank you. The wording was weird in the lecture :)
Equal utility
how was p & 1-p derived?
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).
thanks
Awesome!
thanks very clear
3:59