What is the Nash Equilibrium and why does it matter? | Hacker News Reader

What is the Nash Equilibrium and why does it matter?

economist.com

150 pointsOsiris3034 comments

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

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

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

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.

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?

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.

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/

You might also know Oskari as the author of Buzz Tracker

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

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

I remember the auction - it delayed the intro of 4G as the big players had spent so much money on the auction that they had to sweat their 3G assets to try to recoup their costs.

It worked for the govt - it certainly didn't for the customers...

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).

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

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

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...

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

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.

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 ;)

The whole series on economics is pretty good reading:

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.

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...

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

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.

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

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.

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

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

When does the actual Equilibrium occur?

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

EDIT: Irony is a class with enrollment restrictions.

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).

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.

lol, my exact thought when reading that comment. I think its almost verbatim lifted from the 'Beautiful Mind'.

DING!

Thanks for your participation.

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

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.

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.

Every one of such systems that are non-cooperative, and all players have perfect information (of rules, strategy sets, and associated payoffs).

Rarely does this happen in the real world.

Yeah which is a detail on prisoners dilemma. Again not the thing has the everyday importance.

You sort of have to, since everyone else is doing it.

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