This helped me so much when studying for my exam! The explanation is very clear and concise, making it easy to follow and helps see why it is indeed logical. Thank you so much!!
Personal opinion. The player 1's actions being reveal or hide is kinda confusing, especially when adding the dot line. To make the question more intuitive, the actions can be changed to FIGHT STRATEGY 1 & 2.
11:40 doesn't make sense based on what you said previously about the left side. If P1 deviates, that is reveals when weak, P2 should be under the false impression P1 is strong, and therefore would quit, not fight. This is the same reasoning you used on the left side so I don't see why it does not follow here on the right side. Am I missing something? Thank you
I have a doubt. When you're discussing the profitable deviation for for weak type in the second case, you said that if player 1 would choose to hide its type rather than revealing it, player two would quit giving player 1 a better payoff than what he would get by revealing. But if player 1 does hide, then the probability with which player 2 assumes that whether player 1 is weak or strong would also change. Since player 1 is hiding, as explained before, player 2 would assume that player 1 is weak with the probability of 1 and hence fight and not quit as it did in the first case. But that is not what you have explained.
Don't think about multiple changes at once. If something is an equilibrium, then everyone should believe what is supposed to be happening in equilibrium is actually happening and play accordingly. Equivalently, if someone should *not* believe what is supposed to be happening is actually happening, then those strategies aren't an equilibrium.
Think about it this way: First case If it hides,then it's weak. If it reveals,then it's strong. If it reveals,then it's telling the truth. Second case If it hides,then it's strong. If it reveals,then it's weak. If it reveals,then it's telling the truth. Given this assumptions for first case and second case,you can go back to the game and draw the conclusions.
You should cover a model where information is not revealed also. Your chosen model is not used in our grad courses, nor highly used in Watson's Strategy book.
I'm just curious; what other models are used in your courses? Could you share some problems (or links to them) as well? And finally, how did your classes go (or how are they going)?
why can Player 2 change his strategy in the first equlibrium from "quit" to "fight", but in the 2nd possible equilibrium he has to stay with his strategy "quit" even tough it would have been better for him to choose "fight" instead ? Thank you
I think that in both cases, player 2 was completely confident in her beliefs. Namely, in the first situation, player 2 had complete confidence that anyone hiding would be weak, and in the second situation, player 2 was confident that anyone hiding was strong. If that was indeed the case, then player 2 would have no incentive to switch her strategy when her opponent was hiding or when he revealed himself. I think the important point was that in the first situation, player 1 also did *not* have a profitable deviation. Therefore the first situation constituted a PBE. However, in the second situation, player 1 *did* have a profitable deviation; he could instead hide when he was weak. Therefore the second situation was *not* a PBE.
Thanks for revealing all your information to us!
This helped me so much when studying for my exam! The explanation is very clear and concise, making it easy to follow and helps see why it is indeed logical. Thank you so much!!
How did your exam go?
Personal opinion. The player 1's actions being reveal or hide is kinda confusing, especially when adding the dot line. To make the question more intuitive, the actions can be changed to FIGHT STRATEGY 1 & 2.
I wish I could see a similar explanation of this applied to the case of the Spencer model of education types, which was also an example.
Hello! I'm struggling now with the same thing now. Could you, please, help me if you have time?
@@rosemary8904 this video was the best help I had.
Thank you so much Mr. William Spaniel.
PBE? More like PBJ, because my curiosity and this wonderful information go great together!
This is a great explanation, thanks a lot
Amazing videos, it truly helps.
11:40 doesn't make sense based on what you said previously about the left side. If P1 deviates, that is reveals when weak, P2 should be under the false impression P1 is strong, and therefore would quit, not fight. This is the same reasoning you used on the left side so I don't see why it does not follow here on the right side. Am I missing something? Thank you
I have a doubt. When you're discussing the profitable deviation for for weak type in the second case, you said that if player 1 would choose to hide its type rather than revealing it, player two would quit giving player 1 a better payoff than what he would get by revealing. But if player 1 does hide, then the probability with which player 2 assumes that whether player 1 is weak or strong would also change. Since player 1 is hiding, as explained before, player 2 would assume that player 1 is weak with the probability of 1 and hence fight and not quit as it did in the first case. But that is not what you have explained.
Don't think about multiple changes at once. If something is an equilibrium, then everyone should believe what is supposed to be happening in equilibrium is actually happening and play accordingly. Equivalently, if someone should *not* believe what is supposed to be happening is actually happening, then those strategies aren't an equilibrium.
Think about it this way:
First case
If it hides,then it's weak.
If it reveals,then it's strong.
If it reveals,then it's telling the truth.
Second case
If it hides,then it's strong.
If it reveals,then it's weak.
If it reveals,then it's telling the truth.
Given this assumptions for first case and second case,you can go back to the game and draw the conclusions.
I think it should be strong hides, not reveals since 0.5 > 0.49 and 1 > 0.99
how would you solve this if there was a dotted line/info set connecting P2 on both sides
So pooling equilibrium = The same,
separating equilibrium = something new!
I would maybe say something "different" instead of something "new", but that's a great way to think about it!
Gonna do an ‘ Infranodus’ on this!
You should cover a model where information is not revealed also. Your chosen model is not used in our grad courses, nor highly used in Watson's Strategy book.
I'm just curious; what other models are used in your courses? Could you share some problems (or links to them) as well? And finally, how did your classes go (or how are they going)?
so is an assumption that the P is either 1 or 0 corect or not ?
why can Player 2 change his strategy in the first equlibrium from "quit" to "fight", but in the 2nd possible equilibrium he has to stay with his strategy "quit" even tough it would have been better for him to choose "fight" instead ?
Thank you
I think that in both cases, player 2 was completely confident in her beliefs. Namely, in the first situation, player 2 had complete confidence that anyone hiding would be weak, and in the second situation, player 2 was confident that anyone hiding was strong. If that was indeed the case, then player 2 would have no incentive to switch her strategy when her opponent was hiding or when he revealed himself.
I think the important point was that in the first situation, player 1 also did *not* have a profitable deviation. Therefore the first situation constituted a PBE. However, in the second situation, player 1 *did* have a profitable deviation; he could instead hide when he was weak. Therefore the second situation was *not* a PBE.
Is there an error here?
Shouldn't Player 2 chose quit in the upper right corner after observing reveal..
so wait, what about if the player always reveals or always hides?
just take a look at the next video: #79 and pooling equilibria :)
GOAT
this section is so hard im crying
me too
William in the end.. this is a simple game..
Me :- 😭