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John Nash's Equilibrium Concept In Game Theory (Simplified)
Submitted by Robert Murphy via Mises Canada,
With the tragic deaths (in a taxi accident) of John Nash and his wife, people have been explaining Nash’s contributions to the general public.
The single best piece I’ve seen so far is this one by John Cassidy. However, even Cassidy’s piece doesn’t really make clear exactly how Nash’s famous equilibrium concept works. I’ll give some simple examples in the present post so that the layperson can understand just what Nash accomplished in his celebrated 27-page doctoral dissertation. (Be sure to look at his bibliography on the last page.)
I have seen many commentators tell their readers that John Nash developed the theory of non-cooperative games, in (alleged) contrast to the work on cooperative games by John von Neumann and Oskar Morgenstern. However, it’s a bit misleading to talk in this way. It’s certainly true that von Neumann and Morgenstern (henceforth vNM) did a lot of work on cooperative games (which involve coalitions of players where the players in a coalition can make “joint” moves). But vNM also did pioneering work on non-cooperative games–games where there are no coalitions and every player chooses his own strategy to serve his own payoff. However, vNM only studied the special case of 2-person, zero-sum games. (A zero-sum game is one in which one player’s gain is exactly counterbalanced by the other player’s loss.) This actually covers a lot of what people have in mind when they think of a “game,” including chess, checkers, and card games (if only two people are playing).
The central result from the work of vNM was the minimax theorem. The full details are here, but the intuition is: In a finite two-person zero-sum game, there is a value V for the game such that one player can guarantee himself a payoff of at least V while the other player can limit his losses to V. The name comes from the fact that each player thinks, “Given what I do, what will the other guy do to maximize his payoff in response? Now, having computed my opponent’s best-response for every strategy I might pick, I want to pick my own strategy to minimize that value.” Since we are dealing with a zero-sum game, each player does best for himself by minimizing the other guy’s payoff.
This was a pretty neat result. However, even though plenty of games–especially the ones we have in mind with the term “game”–are two-person zero-sum, there are many strategic interactions where this is not the case. This is where John Nash came in. He invented a solution concept that would work for the entire class of non-cooperative games–meaning those with n players and where the game could be negative-sum, zero-sum, or positive-sum. Then he showed the broad conditions under which his equilibrium would exist. (In other words, it would not have been as impressive or useful if Nash had defined an equilibrium concept for these games, if it rarely existed for a particular n-person positive-sum game.)
For every game we analyze in this framework, we need to specify the set of players, the set of pure strategies available to each player, and finally the payoff function which takes a profile of actual strategies from each player as the input and spits out the payoffs to each player in that scenario. (One of the mathematical complexities is that players are allowed to choose mixed strategies, in which they assign probabilities to their set of pure strategies. So technically, the payoff function for the game as a whole maps from every possible combination of each player’s mixed strategies onto the list of payoffs for each player in that particular outcome.) Now that I’ve given the framework, we can illustrate it with some simple games.
One popular game is the so-called Battle of the Sexes. The story is that a husband and wife have to go either to an event the husband prefers (let’s say it’s an action movie) or an event the wife prefers (let’s say it’s a romantic comedy). But, the catch is that each person would rather watch the movie with his or her spouse, than be alone, and this consideration trumps the choice of the movie. We can (start to) model this story in game theoretic form like this:
- Set of players = {Husband, Wife}
- Husband’s set of pure strategies = {Action, RomCom}
- Wife’s set of pure strategies = {Action, RomCom}
Rather than formally define a payoff function, it’s easier to construct a matrix showing the payoffs to our players from the four possible combinations of their pure strategies, like this (where the husband’s payoff is the first number in each cell and the wife’s payoff comes after the comma):
Let’s make some observations about the above game. First, it’s isn’t a zero-sum game, so the minimax result doesn’t work. In other words, the husband wouldn’t want to approach this situation with the goal of harming the other person as much as possible.
However, the situation is strategic, in the sense that the payoff to each person depends not just on the strategy that person chooses, but also on the strategy the other person chooses. This is what makes game theory different from more conventional settings in economic theory. For example, in mainstream textbook micro, the consumer has a “given” budget and takes market prices as “given,” and then maximizes utility according to those constraints. The consumer doesn’t have to “get into the head” of the producer and worry about whether the producer will change prices/output based on the consumer’s buying decision.
Anyway, back to our “battle of the sexes” game above. Even though the game is positive-sum, there is still the “battle” element because the husband would prefer they both choose the action movie. That yields the best outcome possible for him (a payoff of 3) but only a 2 for the wife. The wife, in contrast, would prefer they both go to the romantic comedy, because she gets a 3 in that outcome (and 3 > 2). Yet to reiterate, they both prefer the other’s company, rather than seeing the preferred movie in isolation (i.e. 2 > 1). And of course, the worst possible outcome–where each gets a payoff of 0–occurs if for some crazy reason the husband watches the romantic comedy (by himself) while the wife watches the action movie (by herself).
In this game, there are two Nash equilibria in pure strategies. In other words, if we (right now, for simplicity) are only allowing the husband and wife to pick either of their two available pure strategies, then there are only two combinations that form a Nash equilibrium. Specifically, the strategy profiles of (Action Movie, Action Movie) and (RomCom, RomCom) both constitute Nash equilibria.
Formally, a Nash equilibrium is defined as a profile of strategies (possibly mixed) in which each player’s chosen strategy constitutes a best-response, given every other player’s chosen strategy in the particular profile.
We can test our two stipulated profiles to see that they are indeed Nash equilibria. First let’s test (Action Movie, Action Movie). If the husband picks “Action Movie” as his strategy, then the wife’s available payoffs are either a 2 (if she also plays “Action Movie”) or a 1 (if she plays “RomCom”). Since 2>1, the wife would want to play “Action Movie” given that her husband is playing “Action Movie.” So that checks. Now for the husband: Given that his wife is playing “Action Movie,” he can get a payoff of either 3 or 0. Since 3>0, he also does better by playing “Action Movie” than “RomCom,” given that his wife is playing “Action Movie.” So that checks. We just proved that (Action Movie, Action Movie) is a Nash equilibrium.
We’ll go quicker for the other stipulated Nash equilibrium of (RomCom, RomCom): If the husband picks “RomCom,” then the wife’s best response is “RomCom” because 3>0. So that checks. And if the wife picks “RomCom,” then the husband’s best response is “RomCom” because 2>1. So that checks, and since we’ve verified that each player is best responding to the other strategies in the profile of (RomCom, RomCom), the whole thing is a Nash equilibrium.
Now for one last example, to show the robustness of Nash’s contribution. There are some games where there is no Nash equilibrium in pure strategies. For example, consider this classic game:
Note that in this game, there is no Nash equilibrium in pure strategies. If Joe plays “Rock,” then Mary’s best response is “Paper.” But if Mary is playing “Paper,” Joe wouldn’t want to play “Rock.” (He would do better playing “Scissors.”) And so on, for the nine possible combinations of pure strategies.
Although there’s no Nash equilibrium in pure strategies, there exists one in mixed strategies. In other words, if we allow Joe and Mary to assign probabilities to each of their pure strategies, then we can find a Nash equilibrium in that broader profile. To cut to the chase, if each player randomly picks each of his or her pure strategies one-third of the time, then we have a Nash equilibrium in those two mixed strategies.
Let’s check our stipulated result. Given that Joe is equally mixing over “Rock,” “Paper,” and “Scissors,” Mary is actually indifferent between her three pure strategies. No matter which of the pure strategies she picks, the mathematical expectation of her payoff is 0. For example, if she picks “Paper” with 100% probability, then 1/3 of the time Joe plays “Rock” and Mary gets 1, 1/3 of the time Joe plays “Paper” and Mary gets 0, and 1/3 of the time Joe plays “Scissors” and Mary gets -1. So her expected payoff before she sees Joe’s actual play is (1/3 x 1) + (1/3 x 0) + (1/3 x [-1]) = (1/3) – (1/3) = 0. We could do a similar calculation for Mary playing “Rock” and “Scissors” against Joe’s stipulated mixed strategy of 1/3 weight on each of his pure strategies.
Therefore, since Mary gets an expected payoff of 0 by playing any of her pure strategies against Joe’s even mixture, any of them constitutes a “best response,” and moreover any linear weighting of them is also a best response. In particular, Mary would be perfectly happy to mix 1/3 on each of her strategies against Joe’s stipulated strategy, because that too would give her an expected payoff of 0 and she can’t do any better than that. (I’m skipping the step of actually doing the math to show that mixing over pure strategies that have the same expected payoff, gives the same expected payoff. But I’m hoping it’s intuitive to the reader that if Mary gets 0 from playing any of her pure strategies, then if she assigns probabilities to two or three of them, she also gets an expected payoff of 0.)
Thus far we’ve just done half of the work to check that our stipulated mixed strategy profile is indeed a Nash equilibrium. Specifically, we just verified that if Joe is mixing equally over his pure strategies, then Mary is content to mix equally over her pure strategies in response. It remains to do the opposite, namely, to verify that Joe is content to mix equally over his pure strategies, given that Mary is doing so. But since this game is perfectly symmetric, I hope the reader can see that we don’t have any more work; we would just be doing the mirror image of our above calculations.
To bring things full circle, and to avoid confusion, I should mention that von Neumann and Morgenstern’s framework could handle our Rock, Paper, Scissors game, since it is a two-person zero-sum game. Specifically, the value V of the game is 0. If Joe mixes equally over his pure strategies, then he can minimize Mary’s expected payoff from her best response to 0, and Joe can limit his expected losses to 0. (The reason I chose a two-person zero-sum game to illustrate a mixed strategy Nash equilibrium is that I wanted to keep things as simple as possible.)
Now that we’ve seen what a Nash equilibrium in mixed strategies looks like, I can relate Nash’s central result in his 27-page dissertation: Using a “fixed point theorem” from mathematics, Nash showed the general conditions under which we can prove that there exists at least one Nash equilibrium for a game. (Of course, Nash didn’t call his solution concept a “Nash equilibrium” in his dissertation, he called it an “equilibrium point.” The label “Nash equilibrium” came later from others.)
Oh, one last thing. Now that we know what Nash did at Princeton, can you appreciate how absurd the relevant scenes from the Ron Howard movie were?
When the movie’s Nash (played by Russell Crowe) tells his friends that they need to stop picking their approach to the ladies in terms of narrow self-interest, and instead figure out what the group as a whole needs to do in order to promote the interest of the group, that is arguably the exact opposite of the analysis in the real Nash’s doctoral dissertation. Indeed, if we analyzed the strategic environment of the bar in the way the movie Nash does so, the real Nash would say, “If all the guys could agree to ignore the pretty blonde woman and focus on her plainer friends, all the guys would be happier than if they each focused on the pretty blonde. But, that outcome doesn’t constitute a Nash equilibrium, so alas, we can’t expect it to work. If the rest of us focused on the plainer friends, we would each have an incentive to deviate and go after the pretty blonde. Ah, the limits of rational, self-interested behavior.”
(I hope the reader will forgive the possibly sexist overtones of the preceding paragraph, but it’s how Ron Howard chose to convey Nash’s insights to the world. I am playing the hand I was dealt.)
John Nash provided economists with a powerful framework for analyzing strategic interactions. If you want to see how economists took his neat result and applied it in settings where it leads to absurdity, read my articles here and here.
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That's as boring as Greece.
And it is about to get paint drying boring, cue the egghead convention in 3..2..1
Why not conspiracy fact?
Nash & wife suicided for valid theorem.
Study other cultures for Fascism/Socialism/Communism takeovers.
Actually Nash's ideas were simplistic. In any group of people each individual has two desires: 1.) Get what he wants. 2.) Failing that, see to it that no one else gets what they want. The "if I can't win then no one else can either" concept.
This explains why when a group is deciding about what type restaurant to go the they decide (as a group) to go to a restaurant the NONE of them would pick first.
People are jerks. Just look at the way laws are made. Or better yet don't think about it.
It's of some use in predicting competitor's actions, as in a reaction to a price cut.
But as you say, people are not necessarily rational or predictable, and in the real world, doo doo happens.
Put your understanding of game theory to the test at http://www.conquerclub.com
Great way to kill time too.
OK, so if I emotionally blackmail my wife into seeing the action flick ("We ALWAYS see the movie you want, and besides, I have to work every day and earn the money for the movie, while you just sit at home on your ass"), and she seethes with silent resentment and I don't get laid for a month, which makes me grumpy and withdrawn so that I don't pay any attention to her except for a grunt or two from behind the computer screen, which in turn makes her cooking skills deteriorate, and her laundry skills deteriorate, and I the retaliate by "accidently" leaving porn on her laptop, and then she retaliates by going to Cabo with her feinds for "fun"...
Who wins? Am I missing something?
Sounds like you just about have the married thing down to a science except you let it go to the point of it costing you money.
Hmm...Describes government. Once the guns are eliminated from the equation, nobody else gives two shits about what other people wnat so long as they personally, are appropriately compensated.
For any given person, it's more like:
WIN or LOSSES(min.) vs. LOSE or LOSSES(max.)
Actually Nash's ideas were simplistic. In any group of people each individual has two desires: 1.) Get what he wants. 2.) Failing that, see to it that no one else gets what they want. The "if I can't win then no one else can either" concept.
it's not simplistic, it's amercian thinking.
european are jealous and steal but those who got never prevent the others to get also...
the "if i cannot, then i won't let you", is fucking american behavior, just check you governement everyday worldwide....
His ideas were not simplistic. You are making the mistake of assuming that his work only covered zero-sum non-cooperative games, and applying a value judgment based on the fact that he establishes the optimal way to approach zero-sum non-cooperative games, whereas his work covered variants other than zero-sum games as well.
Fascist Anti-Christian Communistic Totalitarianism. (Read Satanism) = FACT
http://blogs.telegraph.co.uk/news/damianthompson/100049072/jewish-hostil...
Utter fucking nonsense that yields no real world use. To say that economists use his work as an example of its importance is funny at best. When is the last time an economist predicted anything correctly? Mathematics can not help you to predict the future any better than a gypsy psychic. And it's not tragic when an 87 year old dies.
Mathematics, in the right hands, can indeed predict the future. Gypsy Psychics operate on postdiction rather than prediction. In other words, mathematics is verifiable and metaphysics is dogmatic and unverifiable and fails the test of falsifiability that differentiates the alternative and null hypothesis testing from subjectivist theorizing. One is hard science and the other is pseudo-science. Math trumps the Gypsy so stop, Bangin7GramRocks, and Bang2GramRocks instead. Maybe that will help you think more clearly.
Not shitting on mathematics as a whole. Just the trendy, faddish obsession with Game Theory. Good luck using your cute little theorem to predict how the Greek bullshit will end or when the financial system will collapse. Like I said, no better than a gypsy when it comes to world events and complex things like economies and governments.
I always got the opinion that this site was fond of Game Theory from almost the beginning. I think they try to use it to predict future sales/adoption trends of Bitcoin.
Indeed. Game theory requires that you know the motivations of each player (not to mention that you must actually know about who all is really playing). Then there is means - definitely not equal in most cases. Game theory is just that, theory.
Some men just want to watch the world burn.
Mathematics can only predict the future of mathematic problems. If I add 2+2 next week, what will be the outcome? Not really a prediction, though is it? Math can give you probabilities. Thats it. You can bet the house and farm on that if you want. Not me.
You're wrong. Metaphysics is not dogmatic and it is verifiable SUBJECTIVELY. This is the problem. No one ever wants to put in the time to see if unusual phenomenon or theories are valid through personal experience.
That's probably because nobody is that stupid.
What, you mean like the Chinese when they devoloped martial arts, acupuncture and an entire system of medicine based on energy that can't be quantified but can be experience subjectively. You're right those Chinese and their 3,000 year old practices... what a bunch of dipshits.
Mathematics is the base science upon which all fields of science are built.
Your opinion is worthless.
No shit! But it can't predict everything no matter how many chalkboards you fill. You are a silly motherfucker if you believe that mathematics can predict the future of world events.
Technology, Math and Science are the new Holy Fucking Trinity.
Bosh..
I seem to recall those clever guys at LTCM wrote a number of mathematical models..
" Here we go.. it says to go long Russia and short Italy..."
Oh dear.. wtf happened there..
Mkt is stuffed with clever cunts..
Mathematics might be able to tell you how to get there but it cannot tell you why you want to get there, if you even do at all. If it cannot tell you why or even if, it cannot tell you if you will or not.
Clearly it was much easier to get a PhD back then, as this (27 page) doctoral thesis reads like a 4th year or Master's thesis in Math.
A - D < 0 = QE18 (translated into Fed-ese)
I think zh has a completely flawed idea of the composition of their readership.
Doomsday worshipping, metal hoarding simpletons are not very sensitive of sexism and can rarely comprehend anything about game theory.
Many useless things are quite easy to understand.
It's the over-reliance on models and theory that has made macro-economics a sick and perverted joke.
My game theory is that I have a better payoff (and the funny stuff some women also do but when it's too late and hit the Wall in their 30's) to tell GTFO feminist, white knight, mangina retards and progressists then side with MRA, PUA, and MGTOW and waiting patiently the Western gynocracy her inevitable collapse.
While there is AWALT (All Women Are Like That) some women on other countries are NAWALT (Not All Women Are Like That) not because they are different from their Western/Westernized counterpart (who are AWALT) but because their strong culture turn them NAWALT by default and eventually worth marrying...
If you have understood this somewhat cryptic message you have perfectly understood Nash's Game theory...
Go Asian.
If there's two things a man should do in this life it's:
1. Get to Australia,
2. Marry an Asian (pref Chinese, Japanese, or S. Korean)
If you can do both of those things you have it made.
Problem: Australia is Western country with a lot of toxic culture such as feminism and progressivism.
At least if you want me to "go Asian" tell me to go on Mainland China or Hong-Kong where the culture still keep women in their track and avoid them going wild...
Another Nash's equilibrium: don't marry.
So, if I understand you correctly, "shouldvekilledthem" is just a personal urge towards anger that has nothing to do with averting doomsday but simply with venting your rage on someone who displeases you.
My guess is that game theory would reveal that any strategy that involves interaction with you probably leads to a -1 for the player in question, so far as obtaining any useful cooperation goes.
Ha, so much prejudice.
Wow...you are a dumb fuck...
Zero Sum Game Yeah<
You don't call your wife an old bowser, inform her you've met a young strumpet and jump into the shower leaving a loaded gun in the bedroom drawer.
Game Theory is the equivalent of Angel Theory in Medieval times.
As in how many angels can stand on a pin head.
This bull sh.t is designed to awe people about the mental power of our "Shepards"
Fu.k you "Shepards"
Angels can't stand, they fly.
LESS THAN ZERO (Elvis Costello - 1977)
https://www.youtube.com/watch?v=MHQK3yo9CBA
Musical interlude
The Minimax Theorem is key in Decision Theory/Game Theory and I remember it well from 3rd year Stastistics. My Stats Professor was a student of William L. Hays. Just watched 'A Beautiful Mind' three days ago for the first time and did not realize that Nash was responsible for Minimax Criterion. One learns something every day, eh.
What is truthiness?
I think the Bible summed it up better... if you give it Away, it all comes back 10 times.
and that works for good and bad..
Except that Christians wouldn't know cause most of them don't live like Christ and don't give everything away but do think they will get the ticket to the afterlife because they call themselves Christians. And they think that even though you do give everything away and do live like Christ but not being a Christian you won't make it to the afterlife. Some game theory they have.
You're free to criticism the Christian faith but your ignorance makes you look like a dumbass. You can't judge a religion on your own falsehoods. Saying you need to give everything away to be a christian is like saying you need to eat cake everyday to be a Muslim, its wrong, dumb and not based even slightly on reality.
The Chritian faith whether you hate it or not clearly says you are saved by faith ie by simply believeing that Christ died for you and you recieve the Holy Spirit. So no one can be saved by good works without faith even if they live like Mother Theresa. The stuff you are talking about comes from a fortune cookie.
So according to you -and many other so called Christians- you can be the worst mass murderer EVAR but as long as you accept that Christ died for you and voila, you get a ticket to 'heaven' while a Ghandi or other gooddoer doesn't.
How about trible people in some rainforest somewhere who never heard of Christ or Christianity? They don't go to heaven either? No fair cause they were never informed.
You are just as delusional and bad as these ISIS motherfuckers who think they have the true religion, their version is the only right one and they will go to heaven and the rest not.
You need psychological help. Cause that is what religion is: a need for a 'mother' in life. Grow up.
"What you have done to the least of me, you have done to me". Christ said that.
The bible as you know it was written by people who never met Christ and was written way after his death. And that whole mumbo jumbo of the resurection was invented many years later during a concilium in Rome. Cause hey, a religion where you savior was crucified is not of much use when you want to impress and oppress the masses. That whole story btw. lies at the root of anti-semitism.
Edit: Oh, and I am 'free to criticize Christianity' (thank you very much) because our ancestors fought hard for that right. If I had said this some centuries ago I would have ended up burned at the stake or in a dungeon somewhere. Say these things in the ME about Mo and his brutal religion will indeed end you up like that or in a similar fashion. Cause religion is love and peace after all.
WTF !? You can't be Christian and don't follow The Bible closely. That's the problem with modern christianism, a christianism who is without constraints that now even gays, sluts and women who do abortions can declare themselves Christians...
It's the same to tell that a Muslim or a Jew can eat pork and drink alcohol...
For me since Vatican II this religion have lost all credibility, the problem is that they follow modernity and societal changes even those who are totally against the Christian lifestyle.
Edit: you said that "no one can be saved by their good deed", I must add that you don't even know your own religion then !
The true Christians these days are probably the Eastern Orthodox in Russia, not the Catholics and yet lesser the Protestants...
"You can't be Christian and don't follow The Bible closely"
I have a quote for you. From Martin Luther, the first reformer: "A Christian is under no obligation to observe dead Mosaic scriptures"
you might be Christian, but this affiliation, whatever the denomination, does not give you the right to separate Christianity into "True Christians" and... what? Fake Christians?
a Christian is someone that follows Jesus Christ's teachings. period
your problem with the Catholic or Protestant or Orthodox branches of Christianity are just that: your problem
you think you have a superiour "Christian Lifestyle"? then lead by example
which, if you think about it, is exactly what Jesus did, while for example protecting a few minorities from verbal harassment of the Pharisees, who threw stones at "people not following the right lifestyle"
deeds, not words. specifically, your deeds insteads of your words on the behaviour of others, and their "wrong lifestyles". the difference between Christ and the Pharisees, btw
Who is a Protestant, Catholic and Orthodox ain't Protestant my dear.
Well, I doesn't care (it will collapse too) since I'm not so much into religion (but rather traditional values) but like to point hypocrisy in some of so called religious people and live highly decadent lifestyle (you know the guy who goes to Church and see hookers the week-end or the girl who is highly "devout" marry in the Church and have fucked the entire football team before her marriage) talk about hypocrisy.
I also like to point out that in traditional Christianity interest on money (usury) is forbidden (like in Islam) but Protestant such as your Martin Luther allowed it...
Protestant who now even celebrate gay marriage in the UK...
"Well, I doesn't care (it will collapse too) since I'm not so much into religion (but rather traditional values)"
So to recap you believe in Collapse and Traditional Values and don't care about religion or Christianity
To be frank, I find it fascinating. I wish I could understand it better.
You can have a traditional lifestyle without being Christian or even religious.
I just want to point out that some of the Christians (or any religious group) are more modernist and progressive than some non religious peoples like me (but I still believe in God).
I know for example that some Muslims fuck before marriage and drink alcohol (no joke) and go religiously on the Mosque the Friday !
For the collapse thing: since the traditionalist thinking is a very small minority (their weight in the political spectrum is null), the modern civilization will collapse indeed.
To be precise I'm more on the French René Guénon way of thinking.
Hope it's more clear now.
There is another outcome path.
The husband chooses the romcom with the hope of getting laid later.
Hence the reason that all economics is bullshit, everyone wants to get laid (undefined motives)and they can't account for it in the theory.
Western marriage = high-end(way too expensive) prostitution. It's not a game, it's a trade. Services should be rendered for certain considerations.
The worst about that are sexless marriage, divorce court and child support.
Western marriage is not a zero sum game. Hubbie usually loses whether he stays married or divorces.
Krugman Equilibrium: The more you are wrong the more you need to write articles for the NYT claiming you were right.
So Krudmeister lies long enough, even he believes his own BS?
John von Neumann was a genius and Nash just stand on genius's shoulders like anybody in science.
I should know. I wrote my dissertation long time ago on "Von Neumann Stability Analysis Applied to Non-linear Parabolic Partial Differential equations."
But using Game Theory.... Nash is more well known than yourself because...?
http://www.dailymotion.com/video/x1zucf8_bbc-the-trap-what-happened-to-o...
[BBC - The Trap What Happened To Our Dreams Of Freedom - 1 Of 3 - Fuck You Buddy]
Watch from ~10:30-19:30 if you really want to understand Nash and his idea of game theory. This is a must-see, done by Adam Curtis who also did The Power of Nightmares, another legendary documentary. Fuck You Buddy is the name of the game which would ultimately win Nash his Nobel Prize. Bottom line: paranoid schizophrenics come up with the most paranoid versions of game theory ever devised- even if humans don't actually behave in the way modeled.
Awesome, thank you.
what fucking contribution - to spent your entire life on " Game theory " ?
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which
each participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s).
Getting killed while not wearing a seatbelt in the Taxi,
is a zero sum game Nash and his wife obviously missed.
WR;)
what does game theory say about dying in a dumbass way from failing to wear your seatbelts? x2?
For further reading, may I recommend:
http://www.amazon.com/Prisoners-Dilemma-William-Poundstone/dp/038541580X...
Yes. John von Neumann was a pure, dyed-in-the-wool genius.
Does this mean that Greece is going to default?
I suspect that you were being flippant. But, you know, if you do an Nash Equilibrium game, it would appear that that is the likely result.
Game theory on Wallstreet is that you can fuck up as much as you want and that the taxpayer will bail you out and you won't go to jail.
Another over simplified academic theory that uses complicated looking equations and big words to make it seem that future actions can be predicted. Game theory and economics are worthless to real world interactions. The real world is far to complex and never gives enough information to a bystander to come to a proper conclusion.
The movie problem has more variables than Action or RomCom. The woman's goal is always to maximise her enjoyment. The man's goal is always sex. Men are far more willing to engage in activity alone. Action movie will never be worth 3. The act of taking the wife out has already removed the posibilty of ActionMovie/ActionMovie. The only guaranteed route to sex is RomCom. However Action Movie can be obtained if the man takes the woman out for a nice dinner. The wife may wish to reciprocate and allow the husband to enjoy his movie if she enjoyed dinner. This is only attainable if the woman does enjoy action movies somewhat. It also depends on what type of action movie. Is it a Predator style action movie, a James Bond, or Superhero. You aren't going to get a woman that doesn't really enjoy action movies to see Predator. If she wants to see Predator, Romcom probably wasn't a choice to begin with. If your woman hates action movies, you aren't ever getting your desired outcome.
Rock, Paper, Scissors is not a zero sum game. Psychology will always be more valuable than Game Theory in this instance. Rock is the most commonly thrown hand. It is the easiest to throw and signifies the most strength. Paper is always seen as weakest. Throwing paper against random players will result in the most wins. There is also the question if the game is best two out of three. Throwing rock is always preferable on the first round. If you throw rock you will most likely tie or win.
In reality zero is always the preferable choice because any group choice will result in unwanted consequences for most of the group. The War Games Theorem. The only winning move is not to play.
adr,
Well done post.
Thanks.
You are correct in many ways, especially stating that in the Real World the players a usually strongly biased, while the Theory only deals with non-biased rational and knowledgeable players, so yes it's hard to apply any Math theory to the everyday life, but that does not mean the Theory is useless and we can't learn from it.
If we properly understand it we can Tweak our decisions to better reflect all the possible outcomes and not just narrowly bias our choices pre-hand.
.. but I will tell you what the secret sauce is here, it's not the choices you make, those are almost always predetermined(via bias etc.) but the trick is which choices you are exposing your self to those are much more easily controlled(that is BTW how "they" control us, not by forcing us into any particular choice but by controlling all the choices given to us).
But rock flies right through paper.
https://www.youtube.com/watch?v=MyCa-LHtIKE
game theory works with some rational humans who would set up a neat matrix to make difficult decisiions. i like my econometrics prof's theory odf nash equilibrium. he said, "sometimes decisions that are suppose to be right are wrong and sometimes wrong decisions are right. here, i'll show you." he was fun in a fun with numbers way.
OK so this Article explains pretty well what a "Nash Equilibrium" is so far so good .. but what about the "Nash Maximus(M)" (Russel Crow joke hahah).
Never heard of that?! UhOh .. well let me tell you a "Nash Maximum" is when exactly like the Author states the movie got it wrong when Nash tells everybody that they would win if they went for the less-pretty girls and ignore the most pretty .. then ofc Nash him self goes for the most pretty, as the Author observed.
As this is Exactly the Big-Game the Powers that Be play against us .. they do everything they can to convince us to be happy with what we got and ignore all the luxuries that we could have(that they have) "so everybody wins", "for the greater good", "for the children", "for world peace" etc. and since they own the Media and most Governments they obviously have the advantage. Still if most people understood the game, well maybe things would be a bit different, but that requires IQ which the PtB try to lower as well.
How does this theory square with the fact that humans are instinctively self destructive, and frequently follow strategies that are counterproductive and do not lead to a positive self-serving outcome? Expecting logical, or predictable for that matter, behavior from humans only results in disappointment and disaster.
Imagine the game theory activities if the federal govt ended marriage and child support and simply paid every female a $1000/ month for every kid they had?