What’s a zero-sum game?

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A zero-sum game is a term used in game theory to describe both real games and situations of any kind, usually between two players or participants, in which one player’s gain is compensated by another player’s loss, equal to the sum of zero. For example, if one 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) is equal to zero.

Games where there can be multiple winners are called non-zero sum games and are becoming less common and less applicable in modern life. To be a true zero-sum game, one party’s losses must exactly equal another party’s gains. Because sometimes a loss can be a gain, real life examples are harder to come by.

If someone plays chess in a tournament, every single game is zero-sum, with a winner and a loser. Outside of the game however, the player is given a numerical ranking. This ranking can change significantly if the player loses to someone much lower in rank, but may not change much if he loses to a much higher ranked player. When a single match is actually one of a series with an external ranking, the total result can be a non-zero sum, as wins or losses aren’t the only thing that matters.

It could also be suggested that the zero-sum game is an oversimplified way of looking at something like chess, which is not a game based on probability. A loser can gain as much from his losses as he gains from his wins. She may become a better player because of the loss, so even though the game technically boils down to a winner and a loser, it may be an advantage to lose. Players matched by those with much greater skill might be more interested in learning than winning.

A couple’s argument can be a zero-sum game, but it depends on the couple’s maturity. While you might think there must be a winner and a loser, that’s not always the case. If Mr. and Mrs. Smith are arguing about who will drive to the store, Mrs. Smith may give up and allow Mr. Smith to drive. Consequently, the driver is +1 and the non-driver is -1. Suppose a compromise is reached where Mr. Smith goes to the store and Mrs. Smith comes back. However, each party has a gain equal to the loss. The result is + half and – half, resulting in a zero sum.

If arguments are frequent, however, an analysis of winning or losing a single game may be much less important than an analysis of total marriage. Both couples can be losers from the argument if it creates bad feelings for each other. The sum can quickly drop below zero if two people are constantly grappling with each other.
The term “zero-sum game” can also be extrapolated to the economics and business practices between two countries. Parity of trade is essentially zero sum, as both countries get the same benefit by buying something and giving something up. However, many trading situations are nonzero-sum, and a country loses more than it gains by making a trade. Again, this applies to the big picture. Perhaps the country that trades at a disadvantage gains something intangible, like another nation’s respect and better diplomatic relations. As in chess, where the loser can profit from his loss, a nation that suffers an economic loss in a trading situation can profit in other ways.

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

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