NPR: What's the Opposite of a Zero-Sum Game?

What's the Opposite of a Zero-Sum Game?

Yesterday during Laura's On The Blog segment, she was discussing whether it's possible to blog too much, when she had this exchange with Mike Pesca:

Listen to it again. It gets funnier.

But the question got us thinking...What is the opposite of a zero-sum game? We know there's such thing as a positive-sum game, where sides can both gain or lose at the same time, but that doesn't exactly seem to be the opposite of a zero-sum game. Are we missing something? What's an example of the opposite of a zero-sum game?

Dan Pashman

8:46 AM ET | 05-14-2008 | permalink

Comments (Send a comment)

In mathematics I would say the opposite of anything is the reciprocal. So 1/x, in this case 0, would be indicitive of an infinite-sum game?

That said, there's only 3 possibilities; positive, negative or zero. I don't think you can call any of them an opposite of each other, per se.

Sent by Leigh Cutler | 9:45 AM ET | 05-14-2008

The opposite of a zero sum game is a "hero" sum game. Cut that zero and get with a hero!

Sent by David Williams | 9:52 AM ET | 05-14-2008

1/0 isn't infinite, it's undefined. Attempting to define it as infinite leads to logical fallacies.

The opposite of a zero-sum game is a negative-sum game, in which both sides lose, and whatever they've lost is thrown into an inky abyss, never to be seen again.

Sent by Greg | 10:36 AM ET | 05-14-2008

if a zero sum game is when someone has to lose for someone else to win, then wouldn't the opposite be when no one has to lose for someone else to win, i.e. I can win on my own?

Sent by m.rawlins | 10:55 AM ET | 05-14-2008

the opposite of a zero sum game is either a positive sum game (everyone wins) and a negative sum game (everyone loses).

Sent by Tarah | 11:28 AM ET | 05-14-2008

How about a Total-sum game, where winners and losers are undefined, and you just play for the sake of playing?

Sent by A.Yo | 12:21 PM ET | 05-14-2008

In a mathmatical dialectic. Tarah is correct. However the term "a Zero sum game" is used in conversation as a mathematical metaphor. Therefore I propose: "Love Loss"
In tennis Love means you have nothing.
In Life it means you have it all.
peace
-jonathan

Sent by Jonathan Klein | 12:22 PM ET | 05-14-2008

A zero-sum game is one in which all of the gains of the participants are equally balanced out by all of the losses of the participants, so this question ultimately boils down to: what is the opposite of equality? Mathematically, would be inequality.

That leaves the two options Tarah mentioned, although her definitions are slightly off. A positive sum game just means the overall gains received by the participants are more than the overall cost, even though some of the participants in the game may have clearly lost (the benefit they received didn't offset their cost).

Not that they're bitter or anything.

Sent by kevsmirk | 1:21 PM ET | 05-14-2008

This sounds like an excellent question for Keith Devlin.

I don't think there is a single word answer for this. There is the set of all games and a subset of this is the set of zero-sum games. Other posters have mentioned games that are not zero-sum, but none can be considered opposite in any meaningful sense of the word. What's the opposite of a tortoise shell cat? A black cat? A white cat? A peanut butter and jelly sandwich? I think we have to embrace the notion that some things don't have opposites.

Sent by Dave Wiley | 1:58 PM ET | 05-14-2008

Tarah's right, mostly. Actually, there is no opposite, strictly speaking, to a Zero-Sum Game. A ZSG is the mid point between a Positive-Sum Game (where the sum of everyone's score is positive) and the Negative-Sum Game (where the sum of everyone's score is negative).

Some people might lose in a Positive-Sum Game. Some people might win in a Negative-Sum Game.

Sent by Arthur Klassen | 4:47 PM ET | 05-14-2008

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