
What is meant by a “Zero-Sum Game”? - erik998
https://robertpaulwolff.blogspot.com/2017/04/balm-for-soul.html
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paulddraper
> 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.)

~~~
danjayh
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 :).

~~~
StavrosK
Ooh, is it ad hominem time already?

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friedman23
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.

~~~
pgwhalen
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.

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theprop
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!

~~~
lucio
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.

~~~
theprop
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.

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vilhelm_s
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](http://people.csail.mit.edu/costis/6853fa2011/lec3.pdf)

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erik998
The discussion continues here as well:

[https://robertpaulwolff.blogspot.com/2017/04/initial-
respons...](https://robertpaulwolff.blogspot.com/2017/04/initial-response-
questions-for-i-m-flaud.html)

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known
Globalization is Zero-Sum

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gumby
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.

