Talk:Zero-sum game/Archives/2013

scope of the discussion

Request for general clarification. From the article (and my rudimentary understanding of game theory), it appears that the zero-sum or non-zero-sum status of a game depends on the scope of the discussion. For example, if the universe is closed, all games are ultimately zero-sum because nothing is ever created or destroyed - it's just moved to somewhere else or changed to a different form (energy to matter, e.g.). But clearly games considered on smaller scales can be non-zero-sum; see the example on hunter-gatherer societies I posted above (and which I got from Robert Wright's The Moral Animal).

Games can be truly non-zero-sum, even if you consider the whole universe. If we're dividing up 10 red and 10 black jelly beans, and you prefer the red ones and I prefer the black, then a strategy that gives you all the reds and me all the blacks will be a high payoff for both of us (and a high sum). But a strategy that gives you all the blacks and me the reds will be a low payoff for both of us (and a low sum). The universe can be non-zero-sum because there's no "conservation of happiness" law, nor a "conservation of goal achievement" law. Whether a game is zero sum depends entirely on the payoff matrix, which is a function of the preferences of the players involved. Those preferences aren't required to be "rational" in any sense. They just have to be representable by real numbers. —Preceding unsigned comment added by 140.32.16.100 (talk) 23:01, 25 June 2008 (UTC)

Also take a poker game in which everyone at the table plays to the end, no new players arrive, and everyone plays with the money they brought. There's no house take. For the players as a group, this is a zero-sum game; no money is created or destroyed. But for each player, it is likely to be a non-zero-sum game - odds are each player will either win money or lose money, whether a small amount or large amount. (I am just assuming that it is statistically improbable that any given player will walk away with exactly the same amount of money she brought. That might be wrong, but the point stands for some or most of the players, if not every one of them.)

My understanding is that a zero-sum-game refers to more than one individual, therefore it wouldn't make sense to say that an individual's position is zero-sum in poker. Rather, one would say that poker is either zero-zum (if the house takes no cuts, etc) or non-zero-sum (if there are cuts, etc) Bakerstmd 22:31, 23 May 2007 (UTC)

Even assuming I'm right, I don't know whether this is an insight or a quibble and I would be happy to learn which.

I also wonder whether anyone has used the terms "positive-sum game" and "negative-sum game" for subsets of non-zero-sum game, the former being a win-win game (everyone wins, no one loses) and the latter being a lose-lose game (everyone loses). -- Old Nick 14:21, 26 January 2007 (UTC)

Using the jelly bean game example, the problem with the argument presented is that it takes on a myopic analysis of a scenario with more influencing global variables. Games appear to be zero-sum or non-zero-sum depending on the scope of their analysis i.e., whether all factors that affect the game have been considered.
In the example above, the two individuals have a jelly bean preference, but how do they know they have a preference? Presumably they know because they understand the degree of pleasure or happiness each type (or lack of) of jelly bean induces for them. Therefore, it can be said that the individuals understand what they have to lose which directly leads them to understand what they have to gain. The understanding of the amount of loss and gain is symmetrical since what lead to the understand is symmetrical. This fact leads to the conclusion that the sum of any happiness, sadness, or any other type of emotion in any given scenario must sum to zero since what lead to their understanding was zero-sum.
Continuing off of the example, what if both individuals win their desired beans or what if they both lose and obtain their undesired beans? The chance that they may not get their desired bean is equal to the pleasure of obtaining the bean at the end of the game. The possibility that they may or may not end up with what they desire what allows us to call this a game. Games inherently have to be zero-sum.
Sentient or "feeling" beings have to believe that there are rewards to be had in larger amounts than the losses incurred working for those rewards. Considering this from an evolutionary perspective, an organism that understands that the amount of reward it feels is equal to the amount of labor and toil it feels would be extinct. This may be the reason why it is exceedingly difficult for sentient beings, like humans, to understand such a concept. We are naturally geared towards concluding that the pleasure from our efforts outweigh the lack-of-pleasures of our efforts -- for if this were not the case then what would we do?
What we express externally and fully feel consciously is different from what we feel unconsciously. We need to question what it is that drives sentient beings. Why do we do what we do. --aleksarias (talk) 02:42, 21 February 2013 (UTC)

Proposed move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: page moved (speedily). NW (Talk) 21:20, 11 July 2013 (UTC)

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Zero–sum game → Zero-sum game – The en dash has no earthly business being here. Presumably the article refers to games with a zero sum, as opposed to sum games [noun] with zero. This title came about in March 2011. Marcus Qwertyus (talk) 23:10, 7 July 2013 (UTC)

• Support as speedy move: It is extremely obvious that this needs to be done. —BarrelProof (talk) 06:45, 8 July 2013 (UTC)
• Clear support. This probably could've been a technical move. Red Slash 08:02, 9 July 2013 (UTC)
• Support per reasons above. --Article editor (talk) 02:07, 10 July 2013 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.