zero-sum game

A situation in which a gain by one person or side must be matched by a loss by another person or side: “It's not a zero-sum game in which either youth or pensioners must lose” (Earl W. Foell).

A situation in which one participant's gains result only from another participant's equivalent losses. The net change in total wealth among participants is zero; the wealth is just shifted from one to another.

Investopedia Says:
Options and future contracts are examples of zero-sum games (excluding costs). For every person who gains on a contract, there is a counter-party who loses. Gambling is also an example of a zero-sum game.

A stock market, however, is not a zero-sum game because wealth can be created in a stock market.

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Situation in which the gains of the winners are matched by the losses of the losers. For example, futures and options trading are zero-sum games because for every investor holding a profitable contract, there is another investor on the other side of the trade who is losing money. The total amount of wealth held by all the traders in a zero-sum game remains the same, but the wealth is shifted from some traders to others.

A formal game whereby, on choosing a particular strategy, one competitor's gain is his opponent's loss, gain and loss summing to zero.

A contest in which one player's loss is equal to the other player's gain.

Games may be divided into two classes, zero-sum and non-zero-sum. The class where the sum of the winnings of all the players is the same in all outcomes may be called ‘constant-sum’. But as pay-offs can always be mathematically rescaled, it is convenient and normal to call them ‘zero-sum’. In any change of outcome in a zero-sum game, the gain of the gainer(s) exactly equals the loss of the loser(s). Most games in the ordinary sense, without selective outside intervention, are zero-sum. Chess and football are zero-sum, and remain so even if an outside body awards a fixed prize for winning. But a football game where the participants are bribed to produce a score draw, or a Scrabble game where there is a prize for the highest aggregate score, would be examples of non-zero-sum games. ‘Non-zero-sum’ is preferable to ‘positive-sum’ and ‘negative-sum’. Although these labels are commonly used, they are usually misleading and sometimes wrong, as they fail to specify what the positive sum is being compared with.

In 1944, J. von Neumann and O. Morgenstern proved that all two-person zero-sum games have a unique equilibrium in which each player plays that strategy which minimizes his or her losses for any possible strategy by the other player (see also minimax; maximin). This is mathematically elegant but of limited practical use, although it shows that there exists a unique best strategy for chess. Luckily, that strategy has not yet been found.

The importance of zero-sum games in politics is more informal. In a zero-sum game there is no scope, in the long run, for cooperation among the players, although if there are more than two of them there is much, often infinite, scope for temporary coalitions of some players against the rest. Thus coalition games are zero-sum. Some writers view other political games as zero-sum, for example arms races or industrial conflict(s). This always leads to gloomy prognoses because there is no scope for long-run cooperation.

Non-zero-sum games offer scope for cooperation among the players to achieve one of the outcomes which is best in aggregate. This is true whether the game is regarded as cooperative or non-cooperative. Even in a non-cooperative game such as Prisoners' Dilemma, players may reason about each other's reasoning. In repeated plays of non-co-operative games, they may send each other signals by their actions which enable the players to coordinate their actions on a cooperative (higher) equilibrium (see supergame). Most political games other than coalition games are probably best regarded as non-zero-sum.

A game in which one player's gain is an equivalent net loss to the other player or players. No overall gain is possible. This contrasts with games in which all players can gain, for example by coordination.

A game in which the winnings of some players must equal the losses of the others. Zero-sum games are mentioned in a political context when it is believed that resources are limited, and every decision will produce both winners and losers. In such situations, political decisions will be made on the basis of trade-offs between competing interests.