D.8 Subgame equilibrium | Game Theory - Microeconomics
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- เผยแพร่เมื่อ 5 ต.ค. 2024
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This video shows how to look for a subgame perfect equilibrium. We start by explaining what subgames are, then look for a Nash equilibrium, and finally look for the subgame equilibrium.
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The normal form representation of the game is absolutely wrong. Player 2 must have 4 strategies. L & R are only the actions of player 2, his strategies are LL, LR, RL & RR.
I'm Agree with you
@@florquaranta1 Cant say her wrong completely. she might have assumed simultneous game.
@@faisalsaeed4736 if she assumed a simultaneous game, then the game is displayed wrong in the extensive form. But besides that, she also mentioned that this is supposed to be a sequential game
@@Kevsenkoko Are you saying that there should be a dashed line for player 2's nodes to represent the incomplete information?
Rui Lin Yes! If you want to display this game in the extensive form as a simultaneous game (which can also be interpreted as a game with incomplete information), there needs to be a dashed line between player 2‘s decision nodes.
It finally clicked for me. Thank you, that was well organized and precise.
Hi
according to the solution you show that the sub-game perfect is not Nash equilibrium
D, R in the table. But according to my understand subgame perfect MUST be nash for the initial game
I think your table should have been built with 4 columns LL LR RL RR then you could see that 3,1 is a nash equilibrium
for the game and it is also subgame perfect.
the solution should be
D, LR which means down for player 1 and Left if player 1 choose Up and Right if he choose Down
Absolutely correct what you write: the set of subgame perfect equilibria is a subset of the set of Nash equilibria, or every SPE is a NE (but not every NE is SP). If you evaluate the correct normal form of the sequantila game (that would be a 2x4 game), then you see that two NE in pure strategies exist, one of which is SP. Best to delete this flawed video.
I don’t think it’s wrong, the video points out that you shouldn’t put a sequential game in a 2x2 matrix because you won’t find the correct result, and it’s true, it never says to not put it in a different matrix
Thanks for sharing this information! As some other commenters noted, I don't think the normal form representation is quite right, since this is a sequential game with perfect information. But it was still an interesting discussion.
You saved my life. Thank you
But you can use the matrix for imperfect information (one subgame, or merging player 2's subgames).
why will player 1 choose (3,1)? I didn't understand as up is the dominant strategy for him then why will he choose down ? and why not (5,2) ?
At first when i saw the table, i came up with the same answer as yours. But, this is a sequential game so in order to solve it correctly, we must use the Backward Induction technique.
In short, you can look from the end of the tree game, then sequentially ask:
1- At this point(s), what action will player 2 would choose--> You'll have 2 possible action for player 2
2- Then you can move to player 1 and ask: At this point, what action will player 1 would choose
@@minhucto5108 Can you explain in more details please?
In any sequential game (which mean action of 2nd player can only take action after know the action of the first player, ex: playing chess)
In this case, we have to use backward induction technique:
- Look at the those final decisions of last-making-decision player, and ask: when player 1 choose this decision, what should player 2 choose? --> The outcome would be: Player 2 choose left (2,5) if Player 1 choose Up and choose right (3,1) if player 1 choose Down.
- From those 2 decisions we sure player 2 would take. We assume player 1 is a rational player, and also predict that player 2 would choose that, if player 1 either choose up or down. So player 1 would ask, in those 2 circumstances, which action should I choose to have the best outcome --> the first move decision of player 1 would be down (3,1) player gets 3 benefit, instead of 2 when choose down!
So the outcome should be (3,1)
That's how. Sorrry for making it so long! :)
thank you very much. It was helpful
+ Policonomics, I have a quick question. If the problem can be solved by a 2 X 2 table, then why do we need use to go for a decision tree ? We could have drawn a 2 X 2 table and calculate nash equlibria and solved it.
Dear Diptanil Sengupta,
If you are only looking for the Nash equilibrium in this game, you could have indeed used a 2x2 matrix. However, there's two things that justify the use of a game tree. The first one is that this is a sequential game, which are better represented using game trees rather than matrices. The second reason is that the point of this example is to find the perfect subgame equilibrium (which in this case is not the same as the Nash equilibrium), and this is also easier to do by using a game tree, since it requires a backwards induction.
Thanks for watching!
The Policonomics Team
very interesting! enjoyed it
Thanks +rush B !
7 subgames correction
How you got 2 and 5 ???
god...why my Nash equilibrium is（up，left）
THANK YOU
This is wrong. It’s an incomplete information game. Since p2 does only 1 info set .
how to do a 3x3? game
This was amazing.
good
wrong explanation
That's spectacularly wrong, please delete this video!
Wrong result and explanation🤪
Anyone else here from Ethereal?
wrong
uwu i learn for fun this is a great challenge (and good for cheating)