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

Game Theory 101: The Complete Textbook on Amazon: www.amazon.com/Game-Theory-10...
gametheory101.com/courses/game...
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.

[@leod7154]

seriously, if any of my tutors at university could explain thing so simple like you, life would be a lot easier

[@Gametheory101]

Well, at least we have KZbin.

[@kevinjay5837]

Same feeling for a student having the microeconomics

[@PunmasterSTP]

@@kevinjay5837 How did microeconomics go?

[@Gametheory101]

There is self-interest in cooperating in the stag hunt. There is no self-interest in cooperating in a prisoner's dilemma.

[@csacad2573]

what does that means?

[@ozgeozkose]

It means the players are better off cooperating in the stag hunt

[@ozgeozkose]

Changing your answer in the prisoners dilemma always makes it worse

[@villainsbridgeclub5268]

Soooo... Is Game Theory just applied pessimism?

[@vladmiroshnichenko9679]

This is seriously such an amazingly constructed video that explained everything very clearly. Thank you so much

[@linhtrangpham1995]

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!

[@Gametheory101]

+linh trang pham You're welcome!

[@ItzkatplayzYT]

Love the stag example. Very demonstrative, thank you!

[@angelazhou145]

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 :)

[@belalmatter256]

You are saving my life now! Such a great course !

[@takeruh.6432]

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

[@fladdog]

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.

[@Gametheory101]

Mike Fladlien Thanks!

[@trendnews6761]

Hey, can you please suggest some good economics channel for clearing concepts and learning, actually I am a beginner in economics and wated to know more about engeneering Economics and econometrics

[@Freeflyingpigeon]

I was hoping that someone's atleast mentioned about the time thing.With the no preamble approach, these videos are truly helpful while revising before exams

[@apeironq7281]

really helped me out, thank you so so much, hope to do a great job on upcoming exam all thanks to your videos! ;)

[@ekleanthony7997]

Nice explanation . Thanks for this great work

[@lassman8488]

Ur creating some initial sparks , great work ,dude 👍👍

[@PunmasterSTP]

Stag hunt? More like "nothing but"...amazing educational content. Thanks so much for making and sharing all these videos!

[@Reket11]

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)?

[@yeshasrgowda9060]

your teaching is amazing

[@roumi123]

amazing job dude, thank you very much.

[@Gametheory101]

It's just on Kindle at the moment. (You don't need a Kindle device to be able to read it, though.) I'm going to try to expand it to a print version this summer.

[@tristanpalser7860]

God bless you, I have an exam tm afternoon and this was explained so simply. You are saving my GPA

[@PunmasterSTP]

How did the exam go?

[@dmzrocket]

@@PunmasterSTP the exam was 2 years ago, man might be already secured a nice job 🤣

[@PunmasterSTP]

@@dmzrocket I know, I just love replying to old comments and seeing if they lead to a conversation. I've had a few cool ones so far...

[@rajottam]

OK, so that needs to be factored in. Now, Game theory seems like an extension of logical thinking. Interesting. Thank you for putting things in perspective.

[@navinvijay8075]

Very informative!

[@quicksilver2923]

awesome videos. fun way to spend my free time, hopefully I can keep up :D

[@mostafizrahman3413]

Dear Sir: Thank you very much

[@ElliotScottDating]

Can anyone please use this as an example in dating and relationships? Please ❤️ 🙏

[@Swanidhi]

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?

[@nope242]

Amazing vid

[@RedsoxPats34]

does either player have a dominant strategy?

[@bryceblazegamingyt9741]

This video has amazing quality and microphone quality for its age! Im impressed in the production quality and content!

[@moebiusdroste8293]

You are the best sir

[@samiazaman5240]

Delightful ~

[@Gametheory101]

That's what I'm here for. =) Notation rarely helps.

[@Gametheory101]

We didn't assume the prisoners couldn't work together in a prisoner's dilemma. That was a _result_ of the strategic situation. Players couldn't credibly commit to cooperating there because of their own individual incentive to take the non-cooperative action. Here, cooperative outcomes are possible because if I want to cooperate with you if I know that you will cooperate. That wasn't true in PD.

[@dhruvpathak1850]

Makes sense , yes ! Thank You

[@SilverBlack831]

I don't understand how dominated stratedgy doesn't still apply here. 1 and two, from choosing to hunt the hare, are both better than 0 for choosing to hunt the stag. Doesn't that mean that hare strictly dominates stag?

[@prashantmankani2842]

Isnt there a Nash Equilibrium in the prisoner's dillema video as well (Confess.Confess) ?

[@carlostarragona9450]

what's the difference between 3,3 and 1,1 being nash equilibriums and Pure strategy Nash equilibriums?

[@Vihara87]

Looking at 8:05 is it correct to say that (3,3) is Pareto superior to (1,1)?

[@user-yg1eb6kw5l]

For a beginner it is maybe not obvious if there are strictly dominated strategies present. Maybe can you give a short insight for such a conclusion (rule of thumb)? thank you by the way for the course!

[@mostafizrahman3413]

I want to buy PDF format of this outstanding Game Theory book. Can I ?

[@TheJJSmith92]

So I can download the kindle version and just read it on my pc?

[@SquintStint]

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

[@Gametheory101]

Cheers!

[@Ismi726]

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? Thanks!

[@ronaldsteve2659]

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?

[@Gametheory101]

I'm not sure what exactly you don't understand. Could you be more specific? The two PSNE are equilibria for the reason explained in the video. The MSNE (which is 1/2, 1/2 and not 2/3,1/3) is a MSNE by virtue of the mixed strategy algorithm. So there are three equilibria. Game Theory 101 MOOC (#8): The Mixed Strategy Algorithm

[@Gametheory101]

That's correct.

[@jlistable]

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?

[@aidenstonehouse9651]

Ok so what is the outcome? I am confused. You have said there are to possible choice where they would be technically happy, but what leads them too choose what?

[@marleeallen5242]

Delete other stag and rabbit video.. both are very similar, but this one is a lot better and explains more! :)

[@jim_showi]

thanks lad

[@IsaccLightbournELPASOREALTOR]

3,3 is Pareto efficient. Can it be both Pareto and nash?

[@Gametheory101]

Yup.

[@Odrox]

Oh, I see. I was too thinking as if it were under the "Prisoner's Dilemma" conditions where they would not know if the cooperation would be guaranteed.

[@MicroMartin]

I didn't catch an explanation for the pure part, only standard Nash Equilibrium.

[@chenvenice4960]

Hi Sir, I still don't understand what is a pure strategy? can you explain it as a definition? much thanks!!

[@Ana-wb3jq]

Hey, did you ever figure out this question?

[@pilearn1266]

Is there e book?

[@erikamildred6571]

If this game were played multiple times, I would play "Hare" every time. If the other player picked "Stag" even once, I would be up 2-0, and then if I continued to play "Hare," player two would always be at least 2 points behind me.

[@adamhilmi761]

Thats clever. Would be a hell of a stalemate.

[@minbuk7296]

You explained much better than my Indian PhD professor!!!

[@MrScoodles]

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?

[@ganeshprasad1533]

Does the Nash Equilibrium occur only on principle diagonal?

[@Gametheory101]

No, keep watching and you will find counterexamples.

[@SJ-hz7iu]

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??

[@Gametheory101]

One pure strategy Nash equilibrium is for both players to hunt a stag with certainty. The other is for both players to hunt a hare with certainty. In either case, no one is mixing. Thus, they are PSNE and not MSNE.

[@SJ-hz7iu]

William Spaniel Now I am confused between pure and mixed strategy. Pure strategy is one where user uses same strategy irrespective of what other player makes. So in the case of hunt a stag or hare, each players decision is depending on each other, why is this not a mixed strategy? Lets say if "He" goes for hare, then "She" will also go for hare and if "She'" goes for a stag then "He" does the same. Please explain me how can this be a pure strategy??

[@remavas5470]

Shital Joshi pure strategy is when a player just chooses 1 strategy with 100% probability; mixed strategy is when he chooses more than one strategy with variable probabilities, like e.g. left 30% right 70%

[@remavas5470]

Probably late :P

[@rajottam]

Why could this logic not be applied to the 'Prisoner;s Dilemma' ? Even in that scenario, the outcome for each prisoner improves if he or she knows that the other prisoner isn't going to rat out the other. Here we discussed the possibility of two of them working together, but there we just assumed that they cannot work together. Doesn;t that question the basic assumption that each player doesn't know what the other player is going to do?

[@rajottam]

Hear what William said to me... Here, the players know that if they communicate with each other, there can be a better scenario. They choose to cooperate.

[@REECHUK]

so this game has two solutions? I'd think a rational person would choose hare in this case as you could look at the risk difference and there is the least risk (1 vs 3) and dependancy when choosing the "hare" option.

[@torosalvajebcn]

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

[@anujmishra4412]

Hare Hare box should be 2,2 instead of 1,1 isn't it??

[@yusufselimercan4792]

So, we dont have a definite answer?

[@mr.badaim3975]

Wait I don't get it. Is this Pure Strategy?

[@mangalaekanayake1852]

Good, would be much better if it had been carried out bit slower, Thank you sir

[@t.thomas6967]

Needs pictures of hares

[@a_m7ammad]

there is something I cant understand if there is one stag in the range why stag,stag is 3,3 not 1,1

[@luigimorisco239]

Hi Ali, the numbers in the matrix refers to the expected payoff and not to the number of the outcome, in that way the sense is that if the hunters collaborate to catch the stag, they get a greater payoff (3) than it would be if they deviate and hunt an hare (2). Indeed in the Hp he said that a stag has more meat than two hares, so 2 hares are equal to 4, while one stag for both players is equal to 6 (3 and 3)

[@ashemerson3180]

That's because 1 stag= 6 hares. It is divided into half and each player earns meat equivalent to 3 hares.

[@gustavocardenas2297]

Real life application: Why is a hare worth 2 as an individual catch, but only 1 when it's caught by both hunters?

[@Gametheory101]

Gustavo Cardenas There are multiple hares on the range. If both hunt hares, they will split that amount. If only one hunts hares, that individual will get all of them.

[@gustavocardenas2297]

ah ok. Thanks! Liking the textbook

[@unohu4999]

One player chooses stag, other player chooses hare. Does the stag chooser regret? Of course. Only route to no regrets is choose hare. If other player chooses stag you get 2, if other player chooses hare you get 1, neither way do you go hungry. Pre-arranging, stag is better choice, and that is what humans did and do - they tribalized and agreed in advance to co-operate.

[@Odrox]

But what If getting 0 meat would result in starvation. Then no one would risk picking stag.

[@AvihooI]

Lure the boar! 340 food

[@unknowninfinium4353]

Why Co-Operate? I could be better off with the 2,0 outcome. I care less about the ither guy and 2 is greater than 1.

[@kiwiisflyine865]

Hare Hare should be 2-2 instead of 1-1. Why not ???????????????????????????

[@user-fg3nu3ec4i]

Because each hare gives you 1. If both hunters go for hares there are only 1 for each. If 1 hunter goes for hares, while the other for stag, first hunter will get 2 hares, while the other 0. Just imagine that there are 2 hares and 1 stag for 2 hunters to catch.

[@khondokershafi9203]

can u speak slowly ???????

[@Anadibr]

+khondoker shafi you know you can slow down the speed of the video at the bottom right

[@morgengabe1]

I think 'they' pronouns work just as well. Thanks for these vids nonetheless.

[@DSAK55]

rabbit season, duck season.....