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Zero-sum

From Academic Kids

Zero-sum describes a situation in which a participant's gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). It is so named because when you add up the total gains of the participants and subtract the total losses then they will sum to zero. Cutting a cake is zero- or constant-sum because taking a larger piece for yourself reduces the amount of cake available for others. Situations where participants can all gain or suffer together, such as a country with an excess of bananas trading with an other country for their excess of apples where both benefit from the transaction, are referred to as non-zero-sum.

The concept was first developed in game theory and consequently zero-sum situations are often called zero-sum games though this does not imply that the concept, or game theory itself, applies only to what are commonly referred to as games. Optimal strategies for two-player zero-sum games can often be found using minimax strategies.

In 1944 John von Neumann and Oskar Morgenstern proved that any zero-sum game involving n players is in fact a generalised form of a zero-sum game for two persons; and that any non-zero-sum game for n players can be reduced to a zero-sum game for n + 1 players, the (n + 1) th player representing the global profit or loss.

This means that the zero-sum game for two players forms the essential core of mathametical game theory.

(The two paragraphs above are translated from the French article on zero-sum games)

To treat a non-zero-sum situation as a zero-sum situation, or to believe that all situations are zero-sum situations, is called the zero-sum fallacy.

Economics and non-zero-sum

Non-zero-sum situations are an important part of economic activity due to production, marginal utility and value-subjectivity. Most economic situations are non-zero-sum, since valuable goods and services can be created, destroyed, or badly allocated, and any of these will create a net gain or loss.

If a farmer succeeds in raising a bumper crop, he will benefit by being able to sell more food and make more money. The consumers he serves benefit as well, because there is more food to go around, so the price per unit of food will be lower. Other farmers who have not had such a good crop might suffer somewhat due to these lower prices, but this cost to other farmers may very well be less than the benefits enjoyed by everyone else, such that overall the bumper crop has created a net benefit. The same argument applies to other types of productive activity.

Trade is a non-zero-sum activity because all parties to a voluntary transaction believe that they will be better off after the trade than before, otherwise they would not participate. It is possible that they are mistaken in this belief, but experience suggests that people are more often than not able to judge correctly when a transaction would leave them better off, and thus persist in trading throughout their lives. It is not always the case that every participant will benefit equally. However, a trade is still a non-zero-sum situation whenever the result is a net gain, regardless of how evenly or unevenly that gain is distributed.

Complexity and non-zero-sum

It has been theorized by Robert Wright, and among others, that society becomes increasingly non-zero-sum as it becomes more complex, specialized, and interdependent. As one supporter of this view states:

The more complex societies get and the more complex the networks of interdependence within and beyond community and national borders get, the more people are forced in their own interests to find non-zero-sum solutions. That is, win-win solutions instead of win-lose solutions.... Because we find as our interdependence increases that, on the whole, we do better when other people do better as well - so we have to find ways that we can all win, we have to accommodate each other - Bill Clinton, Wired interview, December 2000.[1] (http://www.wired.com/wired/archive/8.12/clinton.html)

See also

Topics in game theory
Evolutionarily stable strategy - Mechanism design - No-win - Winner's curse - Zero-sum
Games: Prisoner's dilemma - Chicken - Stag hunt - Ultimatum game - Matching pennies ...
Related topics: Mathematics - Economics - Behavioral economics - Evolutionary biology - Evolutionary game theory - Population genetics - Behavioral ecology
[ edit ]
de:Nullsummenspiel

es:Suma cero fr:jeu somme nulle he:משחק סכום אפס nl:Nul-somspel ja:非ゼロ和 fi:Nollasummapeli sv:Nollsummespel

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