Game Theory 101 MOOC (#4): Pure Strategy Nash Equilibrium and the Stag Hunt

Game Theory 101: The Complete Textbook on Amazon:

What happens when we have a game that doesn’t have any strictly dominated strategies? This video introduces the concept of Nash equilibrium. A Nash equilibrium is a set of strategies, one for each player, such that no player has incentive to change his or her strategy given what the other players are doing. This video shows how to find pure strategy Nash equilibria by looking at each individual outcome and checking for profitable deviations.

Nash equilibrium is the most important topic in game theory, so we will spend a lot of time further dissecting it.


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  • these videos are really helpful and i cant believe i can watch these for free on youtube!

    Takeru Huang July 18, 2020 9:35 pm Reply
  • there is something I cant understand if there is one stag in the range why stag,stag is 3,3 not 1,1

    Ali Mohammed July 18, 2020 9:35 pm Reply
  • I understand what you are saying, but you didn't really specify the rules: does each want to get as much points as possible no matter what the other gets, or do they want more points then the other, or do they want as many points as they can collectively get, no matter who gets them? I understand it's option 1? But if it would be option 3, would the 1,1 option still be an NS, if a change wouldn't actually worsen the outcome (they still get 2 points)?

    Reket11 July 18, 2020 9:35 pm Reply
  • God bless you, I have an exam tm afternoon and this was explained so simply. You are saving my GPA

    Tristan Palser July 18, 2020 9:35 pm Reply
  • Needs pictures of hares

    T. Thomas July 18, 2020 9:35 pm Reply
  • So you said we have multiple Nash equilibria and also that the two hunters do not know what equipment would the other hunter bring. How would this equilibria help in making a decision?

    Swanidhi Singh July 18, 2020 9:35 pm Reply
  • Hare Hare box should be 2,2 instead of 1,1 isn't it??

    Anuj Mishra July 18, 2020 9:35 pm Reply
  • Love the stag example. Very demonstrative, thank you!

    Joseph Jay July 18, 2020 9:35 pm Reply
  • Delightful ~

    Samia Zaman July 18, 2020 9:35 pm Reply
  • Wait I don't get it. Is this Pure Strategy?

    Mr. Bad Aim July 18, 2020 9:35 pm Reply
  • Lure the boar! 340 food

    AvihooI July 18, 2020 9:35 pm Reply
  • You explained much better than my Indian PhD professor!!!

    AmazingVideosHD July 18, 2020 9:35 pm Reply
  • I was able to follow this technically but, I don't follow the psychology part. You said, people will have no regrets if they follow a Nash equilibrium but if I brought stag equipment and the other guy didn't, I'd get zero and be pissed. So, I'd probably never do that. Therefore, all the technical procedures are irrelevant, aren't they?

    MrScoodles July 18, 2020 9:35 pm Reply
  • what's the difference between 3,3 and 1,1 being nash equilibriums and Pure strategy Nash equilibriums?

    Carlos Tarragona July 18, 2020 9:35 pm Reply
  • really helped me out, thank you so so much, hope to do a great job on upcoming exam all thanks to your videos! 😉

    Apeiron Q July 18, 2020 9:35 pm Reply
  • thank you so much! It's very easy to follow, especially the real case in the first place that you provide, it helps me understand the application of the nash equilibrium in game theory better. Once again, thanks a lot!

    linh trang pham July 18, 2020 9:35 pm Reply
  • Delete other stag and rabbit video.. both are very similar, but this one is a lot better and explains more! 🙂

    Marlee Allen July 18, 2020 9:35 pm Reply
  • Real life application: Why is a hare worth 2 as an individual catch, but only 
    1 when it's caught by both hunters?

    Gustavo Cardenas July 18, 2020 9:35 pm Reply
  • Hi Sir, I still don't understand what is a pure strategy? can you explain it as a definition? much thanks!!

    Chen Venice July 18, 2020 9:35 pm Reply
  • Sir, Your videos and explanations are outstanding.  I watched Ben Polak lecture at Yale, and your explanations are better.  I also like that you don't waste a second of time.

    Mike Fladlien July 18, 2020 9:35 pm Reply
  • Thank you so much for your game theory videos. Those videos are so much better than my professor's teachings….Just want ed to recognize the good work 🙂

    Angela Z July 18, 2020 9:35 pm Reply
  • In the Stag example I say, "Why split hares?".  Ba dump bump.  I'll be here all weekend!

    Benjamin Olds July 18, 2020 9:35 pm Reply
  • what is the difference between a Nash Equilibrium and a Pure Nash Equilibrium?

    Isaac Cornish July 18, 2020 9:35 pm Reply
  • I think 'they' pronouns work just as well. Thanks for these vids nonetheless.

    morgengabe1 July 18, 2020 9:35 pm Reply
  • Dear William
    Excellent Videos! it is so cool to actually hear someone explain it. Your pace is excellent and makes complete sense. I've suscribed to your channel also! 

    I have a question, this is regarding Pareto Dominance. If a game goes like :
                            Left   Right   player B
    player A  Up     2,2   -30,-1
                  Down  -1,-30  1,1
    What outcome would actually occur in this game?
    My answer : As we can see there are two PSNE's (U,L) and (D,R) however the U,L Pareto dominates D,R as both players recieve higher payoffs. Therefore U,L is the most likely outcome. 

    Is that correct? Could you elaborate more on this if need be?

    Ismail B July 18, 2020 9:35 pm Reply
  • can u speak slowly ???????

    khondoker shafi July 18, 2020 9:35 pm Reply
  • does either player have a dominant strategy?

    A M July 18, 2020 9:35 pm Reply
  • this is really helpful, i also want to ask is there 3 nash equilibria in this example? 1. (Stag, Stag) 2. (Hare, Hare) 3. (  (2/3)Stag+(1/3)Hare , (2/3)Stag+(1/3)Hare )? because i find this on the textbook.. but i dont understsand, may you please help me about it?

    ronald steve July 18, 2020 9:35 pm Reply
  • amazing job dude, thank you very much.

    roumi123 July 18, 2020 9:35 pm Reply
  • I was trying to learn what Nash Equilibrium is (for fun believe it or not) and this video was the best in explaining it (also stag hunt) def. gonna look at more of your vids

    YoshiLover122 July 18, 2020 9:35 pm Reply
  • Just make me correct if I am wrong here. The Topic of this video says Pure Strategy Nash equilibrium. However since none of the strategies are pure i.e. players are using mixed strategies, depending on each other. So, this should be mixed strategy Nash equilibrium instead of one mentioned, right??

    Shital Joshi July 18, 2020 9:35 pm Reply
  • Great course, sir,. just a comment…the prisoner's dilema is just hipothetical, in real life people don´t talk  because they fear retribution, especially mafia members. -yes, they would walk out of jail very fast, but they would end up dead very soon. Crime law number one: no snitches

    torosalvajebcn July 18, 2020 9:35 pm Reply
  • seriously, if any of my tutors at university could explain thing so simple like you, life would be a lot easier

    Leo D July 18, 2020 9:35 pm Reply
  • There is self-interest in cooperating in the stag hunt. There is no self-interest in cooperating in a prisoner's dilemma.

    William Spaniel July 18, 2020 9:35 pm Reply
  • So, I'm just checking if I'm understanding correctly here…In this particular hunt, both players have the same incentive to catch the stag because in all situations, splitting the stag gets you maximum profit. Whereas in the PD case, if you didn't cooperate you could potentially get 0 years in jail as opposed to 1. So there was incentive to not cooperate, while here, cooperating produces the same and maximum benefits for both players?

    Jennifer S July 18, 2020 9:35 pm Reply

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