Mixed Strategies Nash Equilibrium: The Math
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- Опубліковано 2 жов 2024
- This video walks through the math of solving for mixed strategies Nash Equilibrium. Two other sister videos to this are:
Mixed Strategies Intuition: • Mixed Strategies Nash ...
Mixed Strategies Calculus ay To Solve: • Solving Mixed Strategy...
Literally the best explanation of the math portion on youtube, thanks so much!
this helped but how in the world are you gonna put "right" on the left and "left" on the right
😂
Are you acoustic?
Thank you so much, I had my test today and this video helped me tremendously and saved me lots of reading through a hard to make out book.
This is very good I have seen many videos by far the best explanation
Best mixed strategies video I have come across ❤
what can you do when you the p's in the equation cancel each other out. leaving you with no final probability. does this signal a pure strategy as only option. or does this just mean i made a mistake
Very clear and helpful! Thanks!
Óptima explicação!
What is your accent - Canadian/Minnesota???
Fcking amazing woman, thank you!!!!!!!!!!!!!!!!!
Great video!
I would like to watch your videos on the subject of behavioral game theory. I'm actually considering a thesis in that area.
Please please tell how to find pure strategy Nash equilibrium
thank you legend
great video but having both players going either right or left makes it a bit confusing, should've given one of the players the option of going up or down
I honestly just need an example without numbers
Just with letters . Just swapthe corespondind letter , do math , have solution
I did not understand anything about this topic in my class, but you saved my life. Keep doing videos for us, plz.
Very nice explanation, but I am having a hard time to generalize it. Suppose each player has 3 choices: L(left), C(enter) and R(ight). With the same idea you get a linear system of 3 equations for unknowns {pL, pC, pR}. If its solutions is valid because all values are in [0, 1], perfect. But what do you do otherwise? For instance, if you find the solution of the system be pL=-0.4, pC=0.1 and pR=1.3. They add up to 1.0, but they are not right. I am guessing the equilibrium point is somehow in the frontier, a few of these probabilities will be 0 and the associated strategy can be ignored. But how do you calculate this? Moreover, what happens if the players have a different number of choices? Then I am getting too many equations, or too few.
First, eliminate all strictly dominated strategies. If there are none and all 9 cells of the payoff matrix survive, then yes it can be formulated as a system of linear equations.
In the example in the video, for the unknown probabilities in the MSNE, one uses p and 1-p for P1, rather than p_1 and p_2, and uses q and 1-q for P2 rather than q_1 and q_2. In the same way, we can reduce the number of equations in a larger system. For example, if both players have three moves as you describe, then one can use p_1, p_2 and 1-p_1-p_2 for the moves of P1 and q_1, q_2 and 1-q_1-q_2 for the moves of P2.
You've given a more intuitive explanation than my professor, thanks for helping!
ty for the demonstration :)
this helped a lot thank you
Aslo what if it was coordination game,and X greater than 0 is the bias of player 1 to play left
Excellent explanation. Thank you.
What if both players go reyt?
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thanks a lot very nice simple explanation
period ...
PERIODDD LETS GET THIS ECON DEGREEEEE
You're a great teacher thanks so much
GREATNESS!!!!
Thank you so much this was an absolutely incredible video!
Thank you mam !!
the best video!
thank you so very much!!!!!
Where is the 3P coming from?
Move the -2p to the other side
Can I ask for something? If they asked what are p,q probability of player 1 and 2 to play left respectively ,or to play right ? It's the same thing you did right?