
What is the Nash Equilibrium and why does it matter? - Osiris30
http://www.economist.com/blogs/economist-explains/2016/09/economist-explains-economics
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hcarvalhoalves
If you find this article interesting, Coursera's "Competitive Strategy" [1] is
a pretty good introduction on the topic of game theory and how it can be used
as a decision-making framework for business, I've found.

As a case study, I recommend watching this episode of "Golden Balls" [2],
which shows how a player can manipulate a game outcome and defeat the natural
Nash equilibria. This is a classic IMO.

[1]
[https://www.coursera.org/learn/competitivestrategy](https://www.coursera.org/learn/competitivestrategy)

[2]
[https://www.youtube.com/watch?v=S0qjK3TWZE8](https://www.youtube.com/watch?v=S0qjK3TWZE8)

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dmacjam
I would like to recommend one more MOOC that covers different models (economic
models, modelling people behavior, randomness, collective actions -Prisoner's
dilemma, segregation models) and make you start thinking about the world in
term of models.

[1] [https://www.coursera.org/learn/model-
thinking](https://www.coursera.org/learn/model-thinking)

~~~
kornish
If anyone is interested in this course but would prefer to read a book
instead, most of this class draws from "Micromotives and Macrobehaviors" by
Nobel economist Thomas Schelling. The book basically serves as a compendium of
different classes of models, and explores how counterintuitive behavior of the
collective can arrive from perfectly reasonable and rational individual
strategies of the actors.

It kind of reminds me of the explanation of how the crowd at the Hajj crush
(on the front page earlier today) behaved more like a fluid than crowd of
communicating agents because the human density was so high.

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nicolapede
Thanks a lot for sharing it. I have just looked it up on Amazon and found that
they say something like 'before Freaknomics ...'. What is the link between the
two?

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oli5679
Freakonomics is a write up of several economics papers that used a statistical
method called Instrumental Variables for causal analysis.

Schelling's book is a write-up of the theoretical predictions of several
different game-theory models. I didn't notice much overlap between the two.

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dharma1
Here's my boy's work on how to compute ε-Nash Equilibrium in large imperfect
information games. It solved heads up limit Texas hold'em poker

[http://www.jeskola.net/cfr/](http://www.jeskola.net/cfr/)

You might also know Oskari as the author of Buzz Tracker

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keithpeter
Quote from OA

 _" In 2000 the British government used their help to design a special auction
that sold off its 3G mobile-telecoms operating licences for a cool £22.5
billion ($35.4 billion). Their trick was to treat the auction as a game, and
tweak the rules so that the best strategy for bidders was to make bullish bids
(the winning bidders were less than pleased with the outcome)."_

I'm thinking best price for HM Government was paid by UK customers?

C.F. quote below from [1]

 _" The auction confrmed our view that industrial-organisation issues are more
important than the informational issues on which the auction literature has
mostly focused. In particular, the problems of attracting entrants and dealing
with alliances and mergers are likely to remain major preoccupations of tele-
com-auction designers for the foreseeable future. Tackling such problems
sensibly requires high-qualit ymarket research that keeps pace with
developments in an industry that can change its clothes with bewildering
rapidity. We also need more theoretical work on the industrial-organisation
implications of major auctions."_

(Basically the high bids lead to mergers & consolidation)

[1]
[http://www.nuff.ox.ac.uk/users/klemperer/biggestpaper.pdf](http://www.nuff.ox.ac.uk/users/klemperer/biggestpaper.pdf)

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simon0
FYI, the design of those auctions was led by Ken Binmore [1] who is one of the
current leaders in game theory, and has done similar in other countries.
People may find his publications useful reading on this subject.

I know Ken, he's exactly like you might expect a leading academic but is
basically amazing (and very well liked by his students).

[1]
[https://en.wikipedia.org/wiki/Kenneth_Binmore](https://en.wikipedia.org/wiki/Kenneth_Binmore)

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bartkappenburg
Quite disappointing that the article 'explains' the Nash equilibrium (NE)
without going into details of how a NE is reached.

During my econometrics study this explanation helped me to explain it to
others without going in to the mathematical details:

\- Person A needs to decide what the best strategy is for all strategies of B
(circle, on paper, the outcomes for A)

\- Person B has to do the same (circle as well)

NE => look for 'box' (ie. outcome) that has two circles (there could be more!)

This leads to (confess, confess).

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catnaroek
How well does this deal with the case when the optimal strategy is a mixed
strategy?

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antisthenes
It doesn't, because then you'd have to partially circle everything.

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Cieplak
Shout-out to the mythical man who founded the field of game theory, none other
than Johnny von Neumann:

[https://en.wikipedia.org/wiki/Theory_of_Games_and_Economic_B...](https://en.wikipedia.org/wiki/Theory_of_Games_and_Economic_Behavior)

~~~
valarauca1
von Neumann's body of work is so impressive.

Anyone unfamiliar with him should at least glance at this _Known For_ section
on Wikipedia.
[https://en.wikipedia.org/wiki/John_von_Neumann](https://en.wikipedia.org/wiki/John_von_Neumann)

His body of work, breadth of scope, and reach of influence is really only
comparable to Newton, Gauss, or Euler.

Edit: Can't forget Gauss.

~~~
Cyph0n
Neumann is definitely the last true polymath, and in my opinion the greatest
scientist of the 20th century. Coincidentally, I named my new PC at the
university "vneumann" yesterday.

Don't forget Gauss - he has more contributions than any you've listed, and
contributed to a vast number of fields. His 'known for' section is a separate
Wikipedia page ;)

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davidw
The whole series on economics is pretty good reading:

[http://www.economist.com/blogs/economist-
explains](http://www.economist.com/blogs/economist-explains) \- this seems to
include some other stuff (which is doubtless interesting as well) but you can
skip around to find the economics articles.

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nfriedly
Since it wasn't explained in the article, I went looking for what rules the
British used to capture so much money from the 3g spectrum, and found this on
Wikipedia:

> _The auction was conducted in a simultaneous ascending auction, similar to
> the US format with a slight deviation. In the UK 's version of the
> simultaneous individual auction, each high bidder is only allowed to win one
> of the five auctions whereas in the US, many regions have multiple licences
> which multiple bidders can win._

[https://en.wikipedia.org/wiki/Spectrum_auction#United_Kingdo...](https://en.wikipedia.org/wiki/Spectrum_auction#United_Kingdom)

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zump
What's the difference between the Nash equilibrium and the Min-Max algorithm?

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cousin_it
They are equivalent in zero-sum games, but not in non-zero-sum games. For
example, consider a game between Alice and Bob who are sitting on a bomb. Each
of them has three options:

1) Enjoy a nice latte

2) Trigger the bomb, killing both

3) Disarm the bomb, stopping the other from triggering it

The min-max strategy is to disarm the bomb, but there's a better Nash
equilibrium where both players enjoy their lattes.

~~~
xerophyte12932
haha! That's an unusual example but I suppose it works.

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erikb
Isn't that a copy&paste of an article we discussed a few weeks ago? Of course
it is interesting to see that the Nash Equilibrium comes to the same
conclusion as natural instinct: When stuck in the prisoner dilemma you are F'd
as well as the other guy.

But of course it's not the main application. If I remember correctly it is
mostly used to find balanced solutions in complex inter-company or inter-
government exchanges, considering each side's leverage as well as the assets'
values.

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berntb
I'd recommend Dawkins' Selfish Gene for a good non mathematical introduction.

It really changed mine and lots of other people's worldview.

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callesgg
When does the actual Equilibrium occur?

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anacleto
"When everyone in the group do what it's best for himself and the group."

EDIT: Irony is a class with enrollment restrictions.

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proto-n
No, not really. The nash equilibrium occurs when nobody is able to achieve a
better outcome for him/herself when assuming that noone else would change
their strategy with him (no coordination).

This is not neccessarily the best outcome for the market or the players
themselves, see for example the prisoners dilemma (etc).

~~~
callesgg
I don't see how that is helpful at all, that seams like useless information?

To me, i would look at it as a two dimensional plot somewhere there would be a
statistical point which is the point of equilibrium.

Where these processes would statisticly end up.

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untilHellbanned
prisoner's dilemma controls everything, no idea why Nash gets credit. it's
human nature to create narratives like that sadly.

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Buttons840
Nash didn't discover the Prisoners Dilemma, that system obviously has an
equilibrium. What Nash did was prove that EVERY one of such systems has an
equilibrium, regardless of what the details and weights of various rewards and
penalties (etc) are.

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alimw
It is only in the space of "mixed strategies" that there need be an
equilibrium. And in many (most?) cases it is not at all clear how a mixed-
strategy equilibrium might come about. Therefore Nash's result is more limited
than it might at first sight appear.

The Economist's full article (behind the paywall) in fact repeats this claim
that I consider misleading: "Nash showed that every 'game' with a finite
number of players, each with a finite number of options to choose from, would
have at least one such equilibrium."

An equilibrium that does not depend on the notion of mixed strategies is
called a pure-strategy equilibrium. For an example of a game that has no pure-
strategy equilibrium, see
[https://en.wikipedia.org/wiki/Matching_pennies](https://en.wikipedia.org/wiki/Matching_pennies).

