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.
IIt's crucial to watch lecture videos in the proper order to ensure effective learning. This is because the concepts in each video build upon those introduced in previous videos. To help you with this, I recommend visiting my website, www.selcukozyurt.com, for a recommended course outline.

[@miguelsantaclara842]

Dear god you just saved my exam. Thank you angel

[@hemanthverma5473]

Hey Miguel . Can you help me with my exams?

[@RastafarianRussian]

This was extremely helpful and very clear, thank you!

[@peterhsiao9490]

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

[@anukritishankhla3635]

Right

[@jairotrogolo113]

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

[@ohad157]

Best game theory channel ever!

[@reyhanehnikoonejad9208]

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

[@edgarzeledon1173]

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!

[@marisa4942]

Thank you for this video! Helps me to recap quickly :D

[@fatemehentezari2705]

Thank you for such helpful videos :)

[@sublime9525]

This is really amazing.

[@irenezhang3515]

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

[@rickydua7590]

So helpful, thank you

[@johnchung5299]

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.

[@miguelzuzarte3549]

thank you!! You helped a lot!

[@lecothers]

Elinize emeğinize sağlık hocam. Türkiye'den sevgiler

[@RR-og4ut]

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

[@MightShield29]

Thank you man I think I'll just pass my exam with this

[@ranyiwei7619]

so helpful!

[@saruulbuyan142]

Thank you!!!

[@alierdogan2718]

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

[@kritikachawla6101]

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

[@crownedmyself4359]

Why is S2=UD and not S2=D?

[@cengizorun8308]

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.

[@ignaciocanabal3803]

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?

[@burakeroz9743]

HOCAM SIZI COK SEVIYORUM!

[@laibajunaid4469]

Sir can you plz get a video of hybrid equilibria

[@RazV6]

Thx

[@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?

[@selcukozyurt]

Hi Sid! It is just a simple typo (nothing sophisticated about U). Yes, you're right! It must be D not U, as I argued few minutes prior writing U. Thanks for pointing it out. A remark is posted in descriptions.

[@sidddddddddddddd]

@@selcukozyurt Thank you, great. It’s just that I haven’t studied it in deep and even a typo is enough to confuse students like me. Thank you for this great playlist though! :)

[@hemanthverma5473]

@@sidddddddddddddd Hey can you help me with my exams ?

[@jinjurbreadman]

this comment should be pinned

[@NBin5L]

Any suggested book to use along with these lessons?

[@sanchita_9424]

Sir please make a video on cheap talk perfect bayesian babbling equilibrium also

[@mehmetbayraktar69]

Hocam ilk başta teşekürler zahmetiniz için; benim sorum: ayni tür sorun benim profesörüm de gösterdi, ancak ilk hamleyi bende ilk oyuncu yapiyor ve ondan sonra N yapiyor, bu sorunda mi aynı şekilde, anlatığınız gibi mi çözülüyor ?

[@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!

[@YairCat]

I got to this answe as well. I would like to know if it is the correct answer too :)

[@sofiaalejandrabravoruiz4646]

me too!

[@akshatagarwal6776]

It's correct. Even if t_1 chooses to deviate to the left (which we can see trivially due to strict dominance) we can't have a PBE. So yes, there's no PBE w/ (R, R)

[@tidelwaver1]

I believe there is a pooling PBE for right. Doesnt it depend on the value of beta? If beta is sufficiently small (less than 1/3), playing U is player 2's best response to player 1 playing L. So when beta is less than 1/3 (i.e player 2 plays U if player 1 plays L), then type 1 will not deviate from R (u(R) = 2 vs u(L) = 2) and type 2 will also not deviate from R (u(R) = 3 vs u(L) = 0). So (R,R) satisfied sequential rationality provided that beta

[@ricedratiny7796]

what about for mixed

[@burcuozcan6113]

Hocam, çok teşekkür ederim. O kadar güzel anlatıyorsunuz ki videolarınız çok yardımcı oluyor. Bu kadar complicated konuları sizin sayenize anladım. Hocam, rica etsem, job market signaling ve incomplete information bargaining game açıklayabilir misiniz? Elimde anlatımları var ama kafam çok karıştı. Final sınavına hazırlanıyorum. Mümkün mü hocam? Çok teşekkür ederim. Sevgiyle ve sağlıkla kalınız... 😊

[@selcukozyurt]

Evet bu konular icin video cekmeyi dusunuyorum esasinda, fakat suan seyahat dolayisiyla cekim yapamiyorum. Sinavlarinda basarilar, bol sans

[@burcuozcan6113]

@@selcukozyurt Çok teşekkür ederim hocam, Sevgiyle kalınız.. 😊

[@harryduong9330]

Hi professor, I want to ask that if the player 1 didnot disclose his strategy, then how the player 2 knows that (in the first separating example) the player 1 will always play left if he's type 1 and always play right if he's type 2? Hope you can clarify this to me. Thank you so much!

[@jinjurbreadman]

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

[@simransodhi]

u are right

[@tobilori8824]

There is a pooling equilibrium where both types play R also, isnt there? Then Player 2 plays D conditional on observing R (best response to the belief of mu = 1/2), and U conditional on observing L (with the off-equilibrium belief of sufficiently small beta). Then we have Right, Right, Down|Right, Up|Left, mu=1/2, beta= 0 as another PBE. This equilibrium would fail the intuitive criterion I think, but it is still a PBE.

[@anirbanlala4637]

professor, however by refinement 5 (dominance based criteria) and refinement 6 ( equilibrium dominance), miu and 1-miu should both be equal to 0 how can this be possible?

[@javiermostacero1480]

Se puede agregar subtitulos en castellano?

[@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

[@jahnvisingh1341]

hey you can watch part 13 of this same playlist to get a clearer idea how to calculate value of beta or mu

[@jinjurbreadman]

@@jahnvisingh1341 thank you!

[@TheVenusBoy]

What if the nature was different

[@studenthallo2512]

Isn' t S 2 one = D???

[@zhangjockie6784]

yeah I also think so， maybe it's only the professor's mistake in writing

[@pablomartinez5365]

TE QUIERO

[@caio868]

I have some questions: Q1) you start by saying "P2 *can observe* P1's actions but not the P1's types". Just to be consistent with the game theory language (it's my first time learning game theory, ever) wouldn't it be more appropriate to say: -> Question 1.1 "P2 *knows* (because there is common knowledge property) the available P1's actions but *cannot* *observe* P1's types (due to incomplete information because of the presence of Nature)? -> Question 1.2 Thus, what is the precise difference between Incomplete and Imperfect Info? Can I say that Imperfect Info is a *necessary condition* for Incomplete Info? Moreover, when can I state that the game is one of Incomplete or one of Imperfect Info? Q2) Do we need to state that we are using Backward Induction when we start analyzing both Separating and Pooling Equilibrium? Because this is what we always do, right? I am just asking this because I get a bit lost when setting up the game if I don't use the most appropriate definitions. Thank you very much for the help!

[@selcukozyurt]

These are very good questions: If there is any (non singleton) information set in a game tree, then the game is either imperfect info or incomplete info. If Nature is involved (as if it is a player) then the game is certainly incomplete info. However, a game can be both. To be imperfect info game there must be at least one player (obviously other than nature) and starting from this player's single decision node, at least two of his actions should lead to two separate branches that end up in the same info set at some point of the game (i.e., some players can't distinguish this players actions).

[@jhonnybalcazarflores543]

Siento una gran pena. El idioma es una limitante para el avance del conocimiento y la ciencia. Pero muchas gracias profesor.

[@jinjurbreadman]

please wear a gold chain neckalce and tuck it into your shirt. it would help me learn better. thanks

[@amandaz1454]

why do you pay for university when every youtube teacher is better than my uni prof :)

[@user-rk2zv2kg5y]

my professor use 3hours and explain shit... I think that will be better to learn it on youtube 😂

[@krassfass7739]

Swedish playaaa back at it again. keep repine the set ongod 🫡🫡🫡🫡🫡