Game Theory 101 (#64): Bayesian Nash Equilibrium

gametheory101.com/courses/game-theory-101/
In games of incomplete information, a BNE is a set of strategies, one for each type of player, such that no type has incentive to change his or her strategy given the beliefs about the types and what the other types are doing. Essentially, we are generalizing Nash equilibrium to situations where there are multiple types and uncertainty about which one is actually playing the game.

[@kingthanos4964]

This is very clear and straightforward explanation. Thank you sir! It's amazing what you can do in 10 minutes! Sincerely, A struggling uni student

[@PunmasterSTP]

I hope your studies went well after watching William’s videos. How have you been doing?

[@mohemmedansari8664]

Whole set of Game Theory 101 is amazing. This effort takes the learning to a new level. For this lecture I do have a suggestion. It took some time to figure out - as notation used all along for Player 1 and Player 2 in all other lectures was flipped for this lesson. North side player has been taken as Player 1 here which was not the case in all other lessons.

[@njnj7271]

Your videos really helped me to learn faster. I had been following coursera game theory lectures, I found your video crisp and clear. It is easy to understand.

[@CHURCHISAWESUM]

These videos got me through college and got me genuinely interested in game theory, I still am today

[@leonsisuin4987]

thanks i really appreciate.... until i came across this channel i was considering my so called "game theory teacher" a real teacher.....

[@kevinshen7518]

Am currently preparing for a Game Theory final and this video might have saved my grade. Thank you for the clear and concise explanation!

[@PunmasterSTP]

How did your final go?

[@MsNatalie2205]

great lessons, you just saved my grade. thanks !!

[@eliecerzbaez5582]

In 6:48 youd rather say player 1 instead of 2. Anyway, great video!

[@voicesclipsfordiary]

Thank you, Sir! You're a lifesaver.

[@maja8259]

Helps a lot! Thank you

[@_leo3928]

Thanks a lot. Very clear and understandable

[@emilyf7525]

life saving videos during my finals 😂

[@PunmasterSTP]

How did your finals go?

[@tilmannhogrefe612]

Awesome! Thanks for the effort. That really helped!

[@monsegonzalez5723]

If we have mixed strategies, how can we found the BNE?

[@zeroformsora]

If I wanted to list all the possible outcomes of this type of game, how would you go about doing that?

[@djbarraz]

how do you get up = 1/2 and RL = 5/8 at the end??

[@pratyushamrit3025]

in case of incomplete information, do I know what has happened until now?

[@alexcerny5881]

Thanks for simplifying that form of Nash Equilibrium that my lecture's ridiculous notation can't explain.

[@donfox1036]

Again I would like to know what happens as probabilities change. To me that is the central point of Bayesian analysis.

[@albertinejunedin3196]

Hi, just a question: if player two has only one type, how come she has different payoffs in the two matrices?

[@Gametheory101]

Your type might affect my payoffs. For example, suppose everyone knows I am a benevolent KZbin creator. But I don't know whether you are a troll or an interested learner. My payoff for responding to your comments definitely depends on your type.

[@audrey2116]

Just a question : You told us in the previous video that BNE is only used with incomplete information, that is to say if we don't know the payoffs of the other player. But here : we know all the payoffs depending to the type of player. Is it normal? Because then, in a sense, we know the payoffs so it is not "incomplete".

[@PunmasterSTP]

I think that is a really good observation! In this case, I'm pretty sure that the *type* of one player is the last piece of information that the other player would *not* have.

[@boulbebamarzougui9857]

You are the best Thank you very much !!!!

[@hussanmehmood3303]

means in BNE there will be multiple NE one for each type of player ??...correct me if i am wrong ...

[@PunmasterSTP]

I think a Nash equilibrium encompasses a strategy for *each* player. For instance, in the prisoners' dilemma, the NE is . There aren't two separate NE of (for one player) and (for the other).

[@bitanyagebremichael9600]

You Sir, are simply brilliant. Glory To God that I found this video, May The Lord Bless You.🙏🏿

[@joyceliu1430]

so so so much better than 80 percent of my prof

[@gulinasirova3257]

Truly thank you!

[@agrimrana3892]

What if there is no dominant strategy for the a and b players?

[@user-fs5fc1vv7y]

i believe every situation is a knife edge example and therefore everything is 50/50 to happen. either it does or it doesnt. Anyway, what is the knowledge of BNE good for?

[@TheOtherOne122]

lars exams

[@njnj7271]

I am looking to simulate driver's simultaneous game using Bayesian nash equilibrium. I am assuming 4 types of drivers (cautious, normal, aggressive, very Aggressive) and 2 player can be of either type and when 2 drivers meet on road traffic scenario, they may take 3 actions (accelerate, brake or maintain speed). There can be 16 possible combination of players, each combination will further 3*3 gaming matrix. It is becoming complex to define model. Could you please suggest.

[@PunmasterSTP]

Have you tried writing a program to do this, or have you looked for programs or other tools online?

[@emotionalmindedstate]

Did you covered the grey games theory in this video?

[@mightydog03_]

Thks m8. Needed this for school

[@PunmasterSTP]

How'd the rest of your class and the final go?

[@mightydog03_]

@@PunmasterSTP bro how would I remember, I probably failed

[@PunmasterSTP]

@@mightydog03_ Idk I was just curious. How have things been going since then?

[@mightydog03_]

​@@PunmasterSTP Not great, but I'm turning around for my grades and work ethic, at least I'm trying to. It's so that I don't disrespect teachers and my parents, and work more effectively for myself to produce good work on time. Still a work-in-progress.

[@PunmasterSTP]

@@mightydog03_ That sounds good, and I know the feeling. Personally I'm more of a math and science person, and it was English and Spanish that gave me a ton of trouble when I was in school. A lot of times more advanced stuff in reading and writing goes over my head, and it would be cool to have a better understanding of it all, but I just do what I can...

[@aleksymatys8963]

Correct me if I am wrong, but the game you describe seems to be a fully separating equilibrium. = > P1 only chooses to play Down when he is type A and Up for when he is B. What sense does it make for P2 to ever deviate from his best choice given he has a 100% confidence of P1's type, once P1 chooses either A or B??

[@Gametheory101]

This is a simultaneous move game, so P1 can't respond to any observed moves of P2. What you were saying would be the case if this were a sequential game and we were looking for PBE.

[@harshithvurukonda7542]

how to do if there are 3 types of player

[@phdZines]

If you have a two - player game with 3 types, player P1 is Type 1 with the propability p, Type 2 with the propability q and Type 3 with the remaining propability z = 1 - p - q. (It just adds a further dimension to the linear two player - two types problem. In fact, you can solve any combination of Types x Players by using Gaussian Linear solving algorithm)

[@njnj7271]

@@phdZines could you please share some links , even I had to work on something similar

[@hrishikeshpanigrahi2523]

thank you!

[@milesmoore835]

big ups to the g Spanny for this one !

[@adolfhitlerwithoutmustache6907]

This part is really difficult

[@edutube8972]

[@TeMrN1]

I fucking love you

[@PunmasterSTP]

Hip hip hoobaye!

[@cank9859]

may ALLAH god give his blessing kind sir

[@diyawannawenews7626]

!!

[@PunmasterSTP]

!! ?