# What is zero-sum game? Definition, importance and examples

Updated 30 September 2022

Mathematicians, economists and analysts use the term zero-sum game throughout game theory and economic theory. It describes the financial gains of one party that cause an equal amount of loss for the other party. The net change in wealth in these situations is zero since it's neither destroyed nor created, just redistributed. In this article, we discuss what a zero-sum game is, explain where the concept comes from, tell why a zero-sum game is important and show examples of a zero-sum game.

## What is a zero-sum game?

The concept of zero-sum games comes from game theory, a theoretical approach within economics that uses mathematics to understand how rational people make decisions. In a zero-sum game, the game begins and ends with the same total amount of a particular resource. There can be two or more players. As they transact with each other, the players' individual wealth changes but the total wealth among the players does not increase or decrease. This means that a gain for one player necessarily means an equivalent loss for one or more players in the game.

At the end of the game, if you add the gains and losses of every player the answer is equal to zero. This means that no matter how many transactions players decide to have, there is always a net zero change in the total wealth in the game. This is different from other economic models in which conditions can lead to wealth creation and there can be a mutual gain or mutual loss for players.

### Supply and demand

In a zero-sum game, there is more demand for the resource than there is supply. Because game theory uses an economic lens to study how people make decisions, deal with conflict and strategise, zero-sum games can show how players interact when there are finite resources and one player's gain results in another's loss. The total wealth does not change, but through their decision-making and transactions, the players redistribute the wealth between them according to demand and strategy.

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## What are the origins of the concept of zero-sum games?

The concept of a zero-sum game derives from game theory, a type of economic modelling which tries to understand and predict human decision-making, conflict and strategy in different types of situations. The concept of zero-sum has evolved to apply in other fields, too. One example of this is psychology, in which zero-sum thinking describes a situation in which a person believes that their own success comes at the cost of another's failure. In economics, the zero-sum game is useful to examine situations in which there is a finite amount of wealth or resources.

Players cannot create or destroy wealth and the game cannot introduce more resources, but it can redistribute the existing resources. More recent economic models acknowledge that this kind of situation is very rare and more often there can be a mutual gain or mutual loss in financial and economic systems. The zero-sum fallacy describes a situation in which someone presumes that the situation they are in or trying to understand is one of the finite resources, with clear winners and losers, but in reality, it's not zero-sum because there can be mutual gains through wealth creation.

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## Why are zero-sum games important?

The mathematical equations and data produced in zero-sum games can help predict the outcomes of transactions in many industries. In economics, finance and in other commercial settings, zero-sum games can help to understand how people, parties or economic conditions might redistribute finite wealth or resources. In politics and psychology, the concept of zero-sum thinking can help us to understand how people might approach their interactions with other people in their society or how the government may choose to allocate funding to different sectors in the society.

For that reason, zero-sum modelling can have a significant impact on many people. In the real-world context, large companies, economists, governments and those in the financial services sector use zero-sum games to predict outcomes and guide their decision-making, so zero-sum theory can impact many people beyond the immediate parties to the transaction. It can impact entire communities or even countries, as in the example of zero-sum games informing the ways different countries transact with each other in some circumstances.

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## Examples of zero-sum games

Zero-sum games were first used in economic theory and modelling though there are now many real-world applications and examples of zero-sum games. Usually, the zero-sum game theory presumes that all of the players in a zero-sum game are rational and have all the information that's available about the game. You can also call this perfect information. But there are also examples of zero-sum games in which the players do not have perfect or complete, information.

In this part, we'll discuss some real-world and practical examples of zero-sum games to help improve your understanding of when they are in play and how they work. For instance, many forms of gambling are zero-sum games because in gambling, the amount the winner gains is the same as the amount the players gambled or the amount lost by the players who didn't win. We also cover some examples of situations that might seem like they are zero-sum situations but can produce mutual gains or losses and so are not zero-sum:

### Poker

Poker is a good example of a zero-sum game and many poker players use zero-sum modelling to help them be better poker players. In poker, each player bets an amount based on whether they think they have a strong enough hand of cards to win the round. Only one person can win the round. At the end of the round, the winner takes everything that was bet by the other players. They lose and the winner gains, but the total amount that was bet in each round does not change.

In poker, the players do not have perfect information because they don't know what cards are in the other players' hands. This means that poker, like many gambling games, is a zero-sum game that is based on both skill, information and luck. Other card games like bridge and some team sports games, like tennis or football, are good examples of zero-sum games since for one player to win, it's necessary for the other player to lose.

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### Matching pennies

‘Matching pennies' is a common zero-sum game in game theory, the original framework to describe zero-sum games. Economic theorists often experiment with this game to help deepen their knowledge of how mathematics and decision-making play out in a zero-sum situation. Matching pennies is a competition in which two players, A and B, each have a matching coin with a side of heads and a side of tails. To play the game, each player places their coin on a surface in front of them at the same time.

If the coins are both heads or both tails, then player A gets to keep their coin and takes player B's coin. If one coin is heads and one is tails, player B gets to keep their coin and also takes player A's coin. In the matching pennies game, the players have imperfect information because they do not know which side of the coin the other player is going to show. This is useful to economists and statisticians to predict how players in a zero-sum game may decide to play and what strategies may assist them to win the game.

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### Commercial transactions and contracts

Some situations may seem zero-sum, but they are really positive-sum or win-win games. For example, in most commercial transactions, even though only one party might be paying money, there is an exchange between the parties of money for goods or services.

In a fair and transparent transaction, both parties have all of the necessary information about the value of what they are exchanging with the other party. They agree to give away something of theirs in exchange for something another party has and would like to trade. Here, there is no winner and loser and the transaction does not benefit just one party at the expense of the other. Rather, both parties benefit, resulting in a positive-sum situation.

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