Braess’ paradox

[tunesmith]

Another example of the Nash equilibrium being worse than the group optimum is some examples of Tragedy of the Commons, things like overfishing. It's possible to create a model that shows that a more regulated environment leads to more fish per individual than the Nash equilibrium.

I don't think it's appreciated enough that some forms of regulation actually do make things better for everyone, and that acting only in one's own self-interest can lead to results that are provably worse for your own self-interest.

[edanm]

"I don't think it's appreciated enough that some forms of regulation actually do make things better for everyone, and that acting only in one's own self-interest can lead to results that are provably worse for your own self-interest."

As someone who is libertarian-ish, I find that a funny thing to say which doesn't jive with reality. Western countries usually have huge governments with huge amounts of regulation, and the default assumption of almost everyone around me seems to be that regulation is the way to deal with almost anything we don't like.

So saying that it's not appreciated that some regulation makes things better for everyone sounds to me like saying "it's not appreciated enough that clothes make us warm".

(Unless, of course, you're referring only to specific circles, e.g. libertarian economists).

[WildUtah]

some forms of regulation actually do make things better for everyone

Best example is that property rights are such a form of regulation. When it comes to fisheries, wildlife, open public lands, air pollution, and intellectual 'property,' the optimal regulation gets much more complicated.

[stale2002]

Tragedy of the commons is fundamentally different.

This paradox would be like if adding more fish to a pond, caused there to be less fish in the pond.

[peller]

I fully agree with your point, but especially for the specific example you've raised, I think there are some very difficult complications that arise from the (lack of an effective) current global governance model.

For instance, regulations are mostly only effective if they're enforceable. With fishing taking place largely in international waters, and as I understand it, enforcement falling upon the coast-guard-equivalent of whichever country's flag the boat is flying, enforcement would be very difficult.

As far as implementing better regulations, any single nation implementing the good regulations would effectively be putting their own industry at an economic disadvantage (and by extension, their citizens who must pay for the more limited supply) compared to the more lax nations.

We see this with the global climate change debate too; basically every single nation needs to agree at the same time for global progress to be made.

Edit: clarified the first sentence.

[philh]

> acting only in one's own self-interest can lead to results that are provably worse for your own self-interest.

To be precise: everyone acting in their own self interest can be worse for everyone's self-interest, than everyone not doing that. For an individual, acting in your own self-interest is still good for your self-interest, tautologically.

Fundamentally, the problem is that people can take resources for themselves, in a way that damages the total resource pool. Each fish you take is one that can't make more fish. Every car on a road slows down all the other cars.

[whack]

I had a hard time understanding how this could be true, until I read the simple math example presented. The problem seems to be one of externalities. Each individual driver is selfishly optimizing for his own travel time, but by choosing to drive in a short-congested route, instead of a longer-sparse route, he's negatively impacting the travel times of everyone else around him.

It's been well proven in economics that externalities, if unregulated, will produce sub-optimal outcomes. That the way to restore optimal outcomes is to impose a tax that's proportional to the negative externality imposed on others. In an ideal high-tech world, this can be achieved by having differential prices that each driver has to pay, to use each road/highway. In a low tech world, narrowing/closing a road is akin to imposing a tax on certain routes, which explains why it can counter-intuitively help us get to a more optimal outcome.

[alimw]

This is the so-called Pigovian Tax. Also named for Arthur Pigou is a road traffic thought experiment much like Braess's ("Pigou's example").

[Chris2048]

So if I understand it, adding road signs before the new route adding estimated travel times (that take congestion into account) will fix things? The paradox arises from considering only route length, and not congestion?

[beobab]

Presumbly, adding a temporary speed-limit to a road would have a similar effect.

[karmacoda]

An overloaded shortcut is a trap.

[laszlokorte]

The german wiki article has an paragraph about an analogue effect in mechanics in which adding an additional spring to support a hanging weight can causes the weight to hang lower than before. Which I found quite interesting.

[mulmen]

I don't speak German, can you provide a link to the paragraph and/or a translation?

[WhitneyLand]

>if each driver is making the optimal self-interested decision as to which route is quickest, a shortcut could be chosen too often for drivers to have the shortest travel times

Does this just mean people are making bad decisions based on incomplete information?

For example, would this still be a problem if everyone was using Google Maps routing which changes routes based on congestion patterns?

[argonaut]

This applies even with perfect information, as long as drivers are completely selfish.

[trvlngsalesmn]

I learned about this in a course titled Dynamics of Complex Networks and Systems taught by Mark Spong, a robotics control theorist active in dynamical systems research. Ever since learning about Braess' Paradox in that course, I have noticed examples of it in the highways of DFW. The simplest case to spot is where an off-ramp feeds directly to the next on-ramp, creating a "shortcut" for drivers who exit and re-enter the highway.

I've tried to make the case that by closing "key" exits on the highway, we could reduce congestion. But who would be responsible for making that likely unpopular decision?

[obstinate]

They do this on some exits. Speak with your county commissioners, the police, etc. https://www.youtube.com/watch?v=9Ia4pzskae8&list=PLEEC4A6D0A...

[cousin_it]

Yeah. Good road planning in the future should avoid situations where a driver can save 5 minutes by delaying 10 others for 1 minute. Adding new roads can certainly create such situations where they weren't before. You need serious effort to figure it out though, because adding a new road can have lots of other effects as well.

[basicplus2]

This reminds me of the example of the placement of a barrier at an exit to reduce the number of interactions to improve pedestrian flow

http://www.gkstill.com/CV/PhD/Chapter3.html

Scroll down to 3.5.3 Flow through a door.

I can't find the original article I read years ago but it showed a large round barrier to be the most effective, and more than one barrier for larger numbers of people

[cr0sh]

Dang you hit it before me - I was wondering the same thing, and posted about it to another comment here...

[dx034]

That's where variable toll expressways are a great idea. If you add a faster way and equip it with variable tolls, the paradox shouldn't appear. The new way will not be congested (if the toll has no upper limit) and drivers taking the traditional way will experience less congestion.

[cs702]

The Braess paradox applies to all networks, including the Internet, the financial system, FaceBook, etc.

It seems crazy, but interconnecting more nodes to improve efficiency (as measured by travel time, costs, etc.) can paradoxically make the whole network less efficient!

[em3rgent0rdr]

this wiki article seems to get posted every few months... https://hn.algolia.com/?query=%09Braess’%20paradox&type=stor...

[beefman]

See also, the Price of Anarchy [1] and How Bad is Selfish Routing [2].

1 https://en.wikipedia.org/wiki/Price_of_anarchy

2 http://theory.stanford.edu/~tim/papers/routing.pdf

[drewhk]

Hm, can't this be circumvented by pushing towards a correlated equilibrium (https://en.wikipedia.org/wiki/Correlated_equilibrium) instead of a Nash equilibrium?

[Pfhreak]

Is this a function of turbulence? When I think about 'perfect' traffic, I think about a pipe with water flowing through it without eddies. Branch and merge a pipe along its length and you'd introduce all sorts of ripples and turbulence.

[ufo]

IT doesn't have to

https://en.wikipedia.org/wiki/Braess%27_paradox#Example

[zardeh]

Someone who is perhaps better versed in machine learning:

Is there some sort of intuition here that would connect this paradox to the effectiveness of dropout in deep neural networks, or am I drawing connections where there aren't any?

[argonaut]

Having studied both topics (just coursework), I don't think so.

[dksidana]

It will be interesting to see a case where all drivers use real-time traffic updates from services like Google Maps

[xyzzy4]

HN might as well pin this article to the top since it gets reposted so much.

[jayajay]

I benefited from this repost.

[runeks]

"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away."

- Antoine de Saint-Exupery