Game Theory 101 (#75): Screening Games

[@ReeceyP]

I would just like to thank you on all of the work you have put into this series over the years. I have recently been through every one of the episodes, and I am looking forward to the next one. Game theory is something that truly interests me, and I feel that without this series I would've never realized it. Thanks!

[@PunmasterSTP]

I feel exactly the same way!

[@PunmasterSTP]

These videos are so good, that they should give them a...run in theaters? Sorry I can't quite think of the word...

[@youlangzhang4382]

This is the 6th time I go through these videos one by one! Looking forward to your next videos!!

[@NE0KRATOS]

Thank you for this series of videos. I'm working on my Master's thesis on Auction Theory and I wanted a quick recap of Game Theory and this was great. I wish you had done signaling games already, but I'll see my notes for those. Thanks again, your videos were great!

[@PunmasterSTP]

How did your thesis go?

[@NE0KRATOS]

@@PunmasterSTP Hey, thanks for asking! It went great!!

[@PunmasterSTP]

@@NE0KRATOS I'm really glad to hear that!

[@NE0KRATOS]

@@PunmasterSTP thanks, have a wonderful day!

[@ben2591]

I wish you had not stopped before pooling/separating equilibria....

[@aau4688]

When will the remaining videos of PBE be uploaded??

[@flyoten]

How would these PBNE you found at 08:36 be denoted? Thanks!

[@albertchen5501]

Great instructions! I have a question about signaling game although it's not covered yet: what strategy should I select to generate an action in a simulation if there are multiple pure strategy PBE? I'm thinking of playing evolutionary signaling game in multiple time steps where the payoffs is to be updated based on the state variables. Sometimes it is good to find out only one separating or pooling eq. But how about I find both separating and pooling? Then how could the player determine whether or not he/she will reveal the preference type? What about multiple separating and multiple pooling? Maybe my understanding on these equilibria is not perfect. In a simultaneous game with multiple equilibria, I can randomly choose an action; but I don't think that should be the same way for PBE because theoretically there are infinite number of mixed strategy PBE due to infinitely possible belief. And I cannot mix a pooling and separating with different beliefs.

[@viktoriaw1464]

This was a great explanation - thanks for that! But what would happen if p= 1/6? P1 would be indifferent btw. escalating and quitting - but what after that?

[@rusejames7242]

Follow your dreams any mixtures between the two strategies would be an equilibrium

[@matthewblackwell6731]

Do you have or know of any resources that explain simple screening games like this with variables instead of numerical values AND graph or visualize the equilibrium forms? I'm trying to understand the proofs and methods of a paper, "Modeling 'Massive Retaliation'" (Zagare and Kilgour 1993). I thought it would help if I modeled my own simple screening games first but ran into a problem. In the paper, the authors produce a graphical model of the different equilibria forms where the vertical axis is the a priori probability that one state prefers war to capitulation and the vertical is the a priori probability of a challenging state's threat credibility (What if only one state's threat credibility was unknown?). Various thresholds exist on the figure separating peace and war equilibria. As a grad student, I'm struggling to bridge the gap between the technical level of our learning material and the level in papers such as this. If we imagined graphically visualizing equilibria forms for the simple screening game from your video above with variable payoffs and variable weak/strong probability for the one state instead of numerical values, how would you define your axis and thresholds between equilibrium forms? Thanks for all the time and effort you put into your channel and videos, you are very appreciated!

[@Gametheory101]

I wrote a blog post on how I make figures for my articles that might be helpful: williamspaniel.com/2020/08/10/how-to-make-figures-for-formal-articles/ You might also read through some of my papers, especially the more recent ones. I try to make sure there are figures for every important result in papers that I write now.

[@matthewblackwell6731]

@@Gametheory101 Thank you, I was familiar with some of your papers but not the blog. It is an excellent informal resource to understanding the formal research papers out there.

[@베리쌤]

I need more lectures Please~!

[@TheOtherOne122]

im confused at 6:00. Given that it is -.2 how did he end up with 1.2p? How come it is not .8p?

[@Gametheory101]

(1-p)*(-.2) = -.2 + .2p, right? Distribute the negative?

[@BS33875]

Why is that if the payer 1 chooses to quit, player2 still get to choose to fight or concede?

[@s.a.8455]

this is a confusing thing in game theory, especially for begginers. But since Nash Equilibria consist of strategies (which sometimes even contain more actions for one player, if he makes more than one decision during the game) youre nash equilibrium will contain so called "off the nash equilibrium path" actions, actions that wont be reached during the game when the nash equilibrium is played, because the game will end earlier. He talked about that in the videos about how to not write a nash equilibrium. go check that out if you havent

[@alimendez8693]

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