Why didn’t you explain how to determine beliefs in pooling equilibrium? You didn’t even label the beliefs on your game tree. Let’s say Player 2s belief about the likelihood that it’s type A playing left is μL and Player 2’s belief that it’s type B playing left is 1-μL. What does μL need to be greater than or equal to?
In a pooling equilibrium, Player 2's beliefs equal the prior probabilities. If these probabilities are unspecified, then you need to solve for them to determine what values of the probabilities will sustain the equilibrium. If no valid probability values exist (e.g. no values between 0 and 1) that sustain the equilibrium, then the game does not have a pooling equilibrium.
I would like to ask if any type of player 1 or 2 can play a mixed strategy here in your model and under what conditions he can do so. I hope you can give an explanation of how to find a hybrid equilibrium in your model by another video. Thank you
In principle, either player can. Think about the simple cases first. However, in this type of game, you would have to consider Player 1's possible types. By definition, if Player 1 is playing a mixed strategy, then Player 2 would not be able to determine Player 1's type. So, the mixed strategy would have to make Player 2 indifferent between their possible actions, and Player 2's beliefs about Player 1's types would have to be consistent with the prior beliefs. If Player 2 is playing a mixed strategy, then that means Player 2 is making Player 1 indifferent between their possible actions, which means again, that Player 2 can't determine what Player 1's type is. I will put your request on my list of videos to make, but it might be a while until I get to that one. Thank you for your question!
Well, it's part of the equilibrium, but it's player 2's beliefs about Player 1's type when Player 1 engages in off equilibrium play, so you could call it an off equilibrium belief.
by far the best, and most concise video on PBE. Great job!
Thank you! And thank you for watching!
This video is insanely helpful, thank you so much!!!!!
I'm glad you found it helpful, Christopher! Thank you for watching!
Please make more videos on these topics. Extremely helpful
I'll see what I can do. Thank you for watching!
you are the queen ❤
Thank you for the sweet compliment! And thank you for watching!
Very helpful. Thank you!!
Thank you for watching!
Excellent 👍
Thank you for watching!
Great video. Could you go over Price Discrimination
I will add your request to my list! Thank you for watching!
Why didn’t you explain how to determine beliefs in pooling equilibrium? You didn’t even label the beliefs on your game tree. Let’s say Player 2s belief about the likelihood that it’s type A playing left is μL and Player 2’s belief that it’s type B playing left is 1-μL. What does μL need to be greater than or equal to?
In a pooling equilibrium, Player 2's beliefs equal the prior probabilities. If these probabilities are unspecified, then you need to solve for them to determine what values of the probabilities will sustain the equilibrium. If no valid probability values exist (e.g. no values between 0 and 1) that sustain the equilibrium, then the game does not have a pooling equilibrium.
I would like to ask if any type of player 1 or 2 can play a mixed strategy here in your model and under what conditions he can do so. I hope you can give an explanation of how to find a hybrid equilibrium in your model by another video. Thank you
In principle, either player can. Think about the simple cases first. However, in this type of game, you would have to consider Player 1's possible types. By definition, if Player 1 is playing a mixed strategy, then Player 2 would not be able to determine Player 1's type. So, the mixed strategy would have to make Player 2 indifferent between their possible actions, and Player 2's beliefs about Player 1's types would have to be consistent with the prior beliefs. If Player 2 is playing a mixed strategy, then that means Player 2 is making Player 1 indifferent between their possible actions, which means again, that Player 2 can't determine what Player 1's type is. I will put your request on my list of videos to make, but it might be a while until I get to that one. Thank you for your question!
Thank you for your quick and detailed response. Excellent
So the 1/10 is an OFF equilibrium belief, correct?
Well, it's part of the equilibrium, but it's player 2's beliefs about Player 1's type when Player 1 engages in off equilibrium play, so you could call it an off equilibrium belief.
please if you can help me to do an abstract of "An Experimental Test of Equilibrium Dominance in Signaling Games" for Jordi Brandts
i will be thankful
Hello Amine! I am certainly willing to help you understand parts of the paper that might not be clear to you.