14. How to Solve for Perfect Bayesian Equilibrium: Signalling Games (Game Theory Playlist 10)

Remark: Please note that there is a TYPO in 21.05, when I write the pooling strategy profile: Player 2's strategy must be D not U as I already argue this minutes prior writing the strategy profile.

In this episode we apply Requirements 1- 4 that we learned in episodes 5 - 10 to solve for perfect Bayesian equilibrium. The game we use here is an extensive form game with incomplete but perfect information. This example is relatively more complicated than the games we studied in episodes 11-13. It is very similar to the one we studied in episode 12, but this once is more complicated because Player 2 doesn't have dominant strategies.

This game is a standard example of a large family of games that we call Signalling Games. In signalling games we categorize perfect Bayesian equilibrium as Pooling and Separating. In this episode we define what pooling and separating equilibrium are. You can use these concepts and apply the same logic to solve PBE of any signalling game.

[miguelsantaclara]

Dear god you just saved my exam. Thank you angel

[edgarzeledon]

I'm from Costa Rica and my english is really bad but you explain it too clean and I understood everything perfectly (my teacher should watch your videos jajaj) thanks a lot!

[peterhsiao]

Thank you Professor! I think pooling equilibrium STRATEGY for player 2 in the third case is D

[irenezhang]

your videos are super helpful for studying for my game theory exam, thank you very much!

[sidddddddddddddd]

21:05 You explicitly found out that D was the optimal option for player 2 when playing left as u(Up | β=0.5) < u(Bottom | β=0.5) and hence “D” should’ve entered the strategy profile. Please explain why you used U here and everywhere after this?

[cengizorun]

Değerli Hocam, ellerinize sağlık, videolar informative ve kolay anlaşılır olmuş. Bir hususta sorum olacaktı: yaklaşık Min 21:13' civarında de player 2'nin stratejisini U olarak belirlemişsiniz, acaba D olabilirmi? ( daha önce D olarak tepit etmiştiniz) Çok teşekkürler.

[kritikachawla]

For the case 4 that you did not covered for pooling strategies of S1=R for both types. Can you confirm if the PBE is as follows : [S1^T1= R, S1^T2=R, S2=UD, µ=0.5, Beta <=1/3]

[johnchung]

Although you skip discussing how to compute the hybrid equilibrium, I still would like to ask whether any type of player 1 can play a mixed strategy here and how he can do so. I hope you can demonstrate this in another video in the near future.Thank you.

[jinjurbreadman]

21:04 did you mean to write 'U' or did you mean to write 'D'?

[eglaajlafiona]

Hello, this may be a bit late, but for the last case where they both choose right, we don't have PBE because both prefer to deviate to the left, and therefore, there is no pooling equilibrium, right? Or have I missed something?
Thanks in advance!

[ozthewizardd]

Hocam teşekkür ederim. Sağlıcakla kalın ❤❤❤

[charming.amiiii]

what a good video! I have a question, the payoff of the receiver is x o y ?

[RastafarianRussian]

This was extremely helpful and very clear, thank you!

[alierdogan]

Wish you also explain how to draw extensive form at the beginning with a question...

[RR-ogut]

Thank u thank u so much, but please make more videos on this topic. Please please

[ignaciocanabal]

Hi thank you for these videos ! Do you have any recommendation for an applied theory paper where I could see the hybrid or semi-separating equilibrium in greater detail?

[reyhanehnikoonejad]

thanks, you explained it very well and everything was clear.

[lecothers]

Elinize emeğinize sağlık hocam. Türkiye'den sevgiler

[jairotrogolo]

Thank you very much for the good explanations you give :)

[jinjurbreadman]

8:09 when you 'skip this step' could you just put a link to the video where you cover it in the corner? would increase the usefulness of the video enormously