Zero-Sum Game Meaning: Examples of Zero-Sum Games

A zero-sum game describes a relationship, competition, or business deal where one person's gain is the other person's loss. The phrase "zero-sum game" comes from game theory and the notion that if one person wins and the other person loses, this produces a net gain of zero.

Game theory is a theoretical field of study in the social sciences that applies a mathematical model to predict the likely outcomes of a particular scenario. It is often used by people in political science, business, or poker to predict potential outcomes for scenarios in their fields. Game theory simulates a series of real-world, strategic situations through sequential games to predict decision-making processes. The dominant strategy is often for a player to make the choice that benefits them the most, though the best response is usually to cooperate to ensure the most advantageous, symmetric outcome for all players.

Game-theoretic mathematician John von Neumann helped formulate the idea of parties finding equilibrium through a series of two-person, zero-sum games. Along with Oskar Morgenstern, von Neumann wrote a book titled Theory of Games and Economic Behavior (1944), which is the foundational text of the field. John Nash also had a hand in developing the use of game theory through the Nash Equilibrium, which addresses non-cooperative games involving strategic interactions between players (two or more). Game theorists use the term "zero-sum game" to describe games where one player's gain is the other player's loss.

Zero-sum games occur whenever the aggregate gain between winners and losers totals zero.

1. 1. Matching pennies game: The game of matching pennies is often cited as an example of a zero-sum game. In this game, two players place a penny on a table. If the pennies match (meaning they are both heads or both tails) player A wins the game and keeps both pennies. If the pennies do not match (one is heads and the other is tails), player B wins the game and keeps both pennies. The net change of all outcomes will only favor one of the players.
2. 2. Selling damaged goods: A business transaction can be a two-player zero-sum game where one player is the seller and one player is the buyer. If a seller offloads a broken product to an unsuspecting buyer, the seller wins (by getting money) and the buyer loses (by getting nothing of value for that money).

True zero-sum games are rare but occasionally turn up in financial markets like the stock market. The clearest examples of market-related zero-sum games involve stock options and futures contracts. In both circumstances, if the buyer wins, there’s a good chance the seller will lose, and vice versa.

• Stock options: A stock option allows the option holder to purchase stock at a price that tends to be lower than the market price paid by retail investors. For example, if a company offers employees stock options to compensate for a lower salary, the winner of the game depends on how much the stock ends up being worth. If the company stock is worthless, then the employee loses; they would have been better off getting a higher salary. If the company stock proves highly valuable, the employee wins; they received something of far greater value than a cash salary.
• Futures contracts: A futures contract is a financial agreement to buy or sell an underlying asset—typically a leveraged financial instrument or commodity—for a predetermined price at a designated future time. Speculators use futures contracts to bet on the future price of an asset. For example, a speculator who believes that the current price of gold will skyrocket might purchase gold futures at the low market price, then sell the contracts back at a higher contract price to turn a profit.

In a non-zero-sum game, the fortunes of both parties can rise and fall together. The best type of non-zero-sum game is a win-win situation, where both parties benefit from a deal. For instance, if two sports teams trade players with one another and each team satisfies a need, then the trade produces a net positive sum.

A non-zero-sum game can also yield equally negative consequences for both parties—a lose-lose situation. For example, if two sports teams traded players but one team's player got injured and the other team's player chose to retire rather than accept the trade, it would be a lose-lose situation. The net gain would be negative since both parties would have lost something. Zero-sum games always produce a net gain of zero, with one party winning and the other party losing, while non-zero-sum games produce a net positive or net loss.

Get the MasterClass Annual Membership for exclusive access to video lessons taught by the world’s best, including Paul Krugman, Doris Kearns Goodwin, Ron Finley, Jane Goodall, and more.