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What is meant by a “Zero-Sum Game”? (robertpaulwolff.blogspot.com)
38 points by erik998 on May 1, 2017 | hide | past | web | favorite | 18 comments



> I am talking about a made-up phrase, coined more than seventy years ago by John von Neumann – zero-sum game

> I shall now explain to you exactly what “zero-sum game” means in several thousand well-chosen words.

... several thousand words of dubious quality ...

> Under these very restrictive and special conditions – a two person game with a finite set of outcomes in which the players have strictly opposed preferences for compound lotteries of the outcomes – it is possible fairly easily to show that the sum of the utilities assigned by the two players to any outcome or lottery of outcomes will sum to 1.

> In particular, no game or game-like situation with three or more players can be a zero-sum game.

Bullcrap.

Just because von Neumann used "zero-sum game" to describe his conclusions about a certain 2-player game doesn't grant permanent monopoly of the phrase to that exact situation.

---

I shall now explain to you exactly what “zero-sum game” means in several well-chosen words: A zero-sum game is one in which summation of utility among participants is fixed, regardless of choices made.

(The definition exists despite that fact that -- like everything else in economics -- utility aggregatation or utility itself are controversial concepts.)


I skipped to his last paragraph or two, which in only a few hundred words summed up his point. Your sentence is much better -- this man seems to think that he's far more intelligent than the rest of us, and yet he admits to being a Marxist.

I find this to be interesting, since every real-world instantiation of anything resembling Marxism has resulted in widespread famine and poverty. I practice engineering, which deals in applications, and I find it difficult to understand those who cling to a theory without concern for how well practical applications of the theory work out. That's an attitude of willful ignorance, which doesn't strike me as particularly intelligent ... but maybe that's just because I'm so far below his level :).


Ooh, is it ad hominem time already?


So playing devils advocate, what would you say about American capitalism?


Update: It turns out the great von Neumann came back to extend the zero-sum game to other cases https://robertpaulwolff.blogspot.com/2017/04/balm-for-soul.h...


I agree. He's one of those obnoxious philosophers who thinks his new way to show something as not being well-defined proves he's always right.


Quite generous, referring to him as a philosopher. I mistook his 'philosophy' for a bad case of verbal diarrhea. I think he could benefit from George Orwell's rules:

(i) Never use a metaphor, simile, or other figure of speech which you are used to seeing in print.

(ii) Never use a long word where a short one will do.

(iii) If it is possible to cut a word out, always cut it out.

(iv) Never use the passive where you can use the active.

(v) Never use a foreign phrase, a scientific word, or a jargon word if you can think of an everyday English equivalent.

(vi) Break any of these rules sooner than say anything outright barbarous.


The whole article is /r/iamverysmart material.


> A zero-sum game is one in which summation of utility among participants is fixed [...]

[...] at zero. Otherwise it would be a constant-sum game. Otherwise, agree!


It's amazing that there are people that cannot accept that trade is not a zero sum proposition.

If country A produces rice and country B produces meat, country A can trade some rice for some meat from country B. Now both country A and B can enjoy meat with rice which is better than just eating meat or just eating rice. They are both better off than when they started by engaging in trade (the sum is greater than zero).

Now add country C who only produces salt and country C trades salt to both countries A and B in exchange for meat and rice and now they can all enjoy seasoned meat with rice.


Similarly, a ton of financial trading, especially derivatives. What people fail to realize is that these exchanges of value exist because the buyer often values something more than the seller does, not the exact same amount. In that sense, trade is creating value by allowing that difference to "realize itself," so to speak.


Meaning is simply usage...in the mathematical sense, Von Neumann's definition may be what is technically a zero sum game, but in general political and economic discussions, zero sum game does have a clear and fairly precise meaning.

In general discussion then, a zero sum game is some game or other activity in which resources are not grown or created but simply moved between different parties or re-allocated such that when someone wins, someone else loses.

I would argue that it's EXTREMELY important that we understand that meaning as I think it's the cornerstone of Trump's world-view. He comes from a deal-mentality driven business i.e. you negotiate to your advantage. For most of his real estate purchases, no value was created, his value was simply that he negotiated a better deal. He has negotiated some amazing deals from what I have seen, ridiculously cheap prices for some properties.

The problem with this worldview is that you see the world in terms of winners and losers, not as a dynamic shifting environment. So if you ban coal, for example, then coal miners have lost out...you don't see that they could all and probably do have jobs in solar energy, which incidentally is work that doesn't severely cripple their health. It's a mentality that you can negotiate your way to wealth. While that can work for an individual, it will not work for a country let alone the world!


Don't be silly, the guy is a constructor. He did make money by creating value, which a -well planned building- is a prime example of. The "deals" are to create a lot of value with as fewer resources as you can.


Yes, some of his deals are where he built buildings. Even there, it was a matter of getting some tax credit or very good deal on the land or something that essentially transferred resources to him instead of to someone else. It's not easy to get the buildings built that he's done...he's definitely added value in many cases, but many of them were structured in ways such that he could not lose money (i.e. no real risk, zero sum thinking).

Many of his deals were simply buying existing properties which is what I'm referring to.


The point that I would stress is that 2-player and n-player zero-sum games have very different properties.

2-player zero-sum games are interesting because it's one of the few cases where game theory makes a unique prediction. In general 2-player games there can be multiple Nash equilibria, and the theory does not tell us which one will be chosen. In a zero-sum 2-player game, the only equilibrium strategies are the minimax-ones, which can be directly computed. Also, by inspecting the minimax strategies we can tell that there is no possibility of bargains, there is no role for cheap talk, etc etc. This is where the informal connotations of a "zero sum game" comes from: it's dog-eat-dog and cold hard randomness.

But in n-player games, assuming that the payoffs sum to zero does not lead to any particularly interesting consequences. Any general n-player game can be encoded as a zero-sum (n+1)-player game[0], so all the general subtleties of game theory comes back into play.

For example, consider n pirates that need to split a chest of gold. The sum of payoffs is fixed (it's the number of coins), but still there is a large rule for "politics", i.e. talk to form coalitions, etc. There are a lot of Nash equilibria of the "the three of us gang up on the two of them", and no way a priori to figure out which one will be chosen.

[0] http://people.csail.mit.edu/costis/6853fa2011/lec3.pdf



Globalization is Zero-Sum


Umm, so what other connotation or inference could there be to the phrase "zero sum game?"

What he's really saying, in a roundabout fashion, is that the economy and trade are zero sum and that Obama and Krugman are (respectively) wrong.

I'd say Wolff is the one who's wrong. But he does agree with Trump.




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