What is a Zero Sum Game?

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  • Written By: Tricia Ellis-Christensen
  • Edited By: O. Wallace
  • Last Modified Date: 05 June 2017
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A zero sum game is a term used in game theory to describe both real games and situations of all kinds, usually between two players or participants, where the gain of one player is offset by the loss of another player, equaling the sum of zero. For instance, if a person plays a single game of chess with someone else, one person will lose and one person will win. The win (+1) added to the loss (-1) equals zero.

Games where there can be multiple winners are called non-zero sum, and they are becoming less common and less applicable in modern life. To be a true zero sum game, losses of one party have to be exactly equal to gains of another party. Since sometimes a loss can be a gain, real life examples are more difficult to find.

If someone plays chess in a tournament, each individual match is zero sum, with one winner and one loser. Outside of the game, however, the player is given a number ranking. This ranking can change significantly if the player loses to someone of a much lower rank, but it may not alter much if she loses to a much higher-ranking player. When a single game is actually one in a series with an outside ranking, the total result may be non-zero sum, since wins or losses are not the only thing that count.

It could also be suggested that the zero sum game is an extremely simplified manner of looking at something like chess, which is not a probability-based game. A loser may gain as much from her losses as she does from her wins. She may become a better player as a result of losing, so though technically, the game comes down to one winner and one loser, it may be an advantage to lose. Players matched against those with much greater skill may be more interested in learning than winning.

A couple's argument may be a zero sum game, but it depends on the maturity of the couple. While it might be thought that there has to be one winner and one loser, this is not always the case. If Mr. and Mrs. Smith are arguing about who will drive to the store, Mrs. Smith might give in and allow Mr. Smith to drive. As a result, the driver is +1 and the non-driver is -1. Suppose a compromise is reached where Mr. Smith drives to the store and Mrs. Smith drives back. Still each party to the argument has a gain equal to the loss. The result is + one-half and - one-half, resulting in a zero sum.

If arguments are frequent, however, an analysis of winning or losing in a single match may be far less important than analysis of the total marriage. Both couples may be losers by the argument if it creates mutual bad feelings. The sum can quickly sink below zero if two people are constantly at each other’s throats.

The term "zero sum game" may also be extrapolated to economics and the trading practices between two countries. Equal trade is essentially a zero sum, as both countries gain equal advantage by acquiring something and by giving something up. Lots of trade situations are non-zero sum, however, and one country loses more than it gains in making a trade. Again, this applies to the overall picture. Perhaps the country that trades at a disadvantage gains something non-tangible, like the respect of another nation and better diplomatic relations. As in chess where the loser may profit by his loss, a nation that takes an economic loss in a trading situation may profit in other ways.

In diplomatic relations, there can be win-win, instead of win-lose situations. People or countries may equally benefit without losing. Usually, however, diplomacy comes down to compromise, both parties giving up something to gain something. When the things given up are fairly equal to the things gained, this is still a zero sum game. Negotiation and diplomacy are often called “spreading the pain evenly.”


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Post 5

George Carlin said, " Life is a zero sum game."

What did he mean?

Post 4

Is chess a good example of a zero-sum game? Since a stalemate/draw is possible?

Post 3

This explanation is well written. However i'm still interested on how to implement this theory to HRD or learning and development?

Post 2

For someone looking for a definition/explanation of the term, this serves very nicely and with the +1/-1 used makes the concept clear and easy to grasp. The comment above is interesting as a jumping off point for discussing political economic theories, but that is not the only place this term is used.

Post 1

This explanation presents a somewhat contrived view of the sum in a zero sum game. There are more interesting concepts to describe than just a value of +1 for a winner and -1 for a loser.

For instance, consider poker as a zero-sum game. If each of five players brings $200 to the table, there is still $1,000 among the players at the end of the game, it just is distributed differently among the players.

In political terms, socialists consider national economies as a zero-sum game (if A grows $5,000 richer, it is because this wealth was extracted from some number of victim Bs); whereas capitalists consider economies a nonzero-sum game (human enterprise actually creates new wealth far out of proportion to any transfers or resource depletions; and voluntary transactions address the preferential desires of both parties).

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