Zero-Sum Game Definition in Finance, With Example (2024)

What Is a Zero-Sum Game?

Zero-sum is a situation, often cited in game theory, in which one person’s gain is equivalent to another’s loss, so the net change in wealth or benefit is zero. A zero-sum game may have as few as two players or as many as millions of participants.

In financial markets, options and futures are examples of zero-sum games, excluding transaction costs. For every person who gains on a contract, there is a counter-party who loses.

Key Takeaways

  • A zero-sum game is a situation where, if one party loses, the other party wins, and the net change in wealth is zero.
  • Zero-sum games can include just two players or millions of participants.
  • In financial markets, futures and options are considered zero-sum games because the contracts represent agreements between two parties and, if one investor loses, then the wealth is transferred to another investor.
  • Most transactions are non-zero-sum games because the end result can be beneficial to both parties.

Understanding Zero-Sum Games

Zero-sum games are found in many contexts. Poker and gambling are popular examples of zero-sum games since the sum of the amounts won by some players equals the combined losses of the others. Games like chess and tennis, where there is one winner and one loser, are also zero-sum games.

Derivatives trades are also often cited as zero-sum games, since every dollar earned has to be lost by another party to the transaction.

Zero Sum vs. Positive Sum Games

Zero-sum games are the opposite of win-win situations—such as a trade agreement that significantly increases trade between two nations—or lose-lose situations, like war, for instance. In real life, however, things are not always so obvious, and gains and losses are often difficult to quantify.

When applied specifically to economics, there are multiple factors to consider when understanding a zero-sum game. A zero-sum game assumes a version of perfect competitionand perfect information; both opponents in the model have all the relevant information to make an informed decision. Taking a step back, most transactions or trades are inherently non-zero-sum games because when two parties agree to trade they do so with the understanding that the goods or services they are receiving are more valuable than the goods or services they are trading for it, after transaction costs. This is called positive-sum, and most transactions fall under this category.

Many well-known game theory examples like the prisoner’s dilemma, Cournot Competition, Centipede Game, and Deadlock are also non-zero sum.

A positive sum game is where the net result is greater than zero, even though there may be some winners and losers. In economics, trade and exchange are thought to be examples of a positive sum game.

Zero-Sum Games and GameTheory

Game theory is a complex theoretical study in economics. The 1944 groundbreaking work “Theory of Games and Economic Behavior,” written by Hungarian-born American mathematician John von Neumann and co-written by Oskar Morgenstern, is the foundational text. Game theory is the study of the decision-making process between two or more intelligent and rational parties.

Game theory can be used in a wide array of economic fields, including experimental economics, which uses experiments in a controlled setting to test economic theories with more real-world insight. When applied to economics, game theory uses mathematical formulas and equations to predict outcomes in a transaction, taking into account many different factors, including gains, losses, optimality, and individual behaviors.

In theory, a zero-sum game is solved via three solutions, perhaps the most notable of which is the Nash Equilibrium put forth by John Nash in a 1951 paper titled “Non-Cooperative Games.” The Nash equilibrium states that two or more opponents in the game—given knowledge of each others’ choices and that they will not receive any benefit from changing their choice—will therefore not deviate from their choice.

Example of a Zero Sum Game

The game of matching penniesis often cited as an example of a zero-sum game, according to game theory. The game involves two players, A and B, simultaneously placing a penny on the table. The payoff depends on whether the pennies match or not. If both pennies are heads or tails, Player A wins and keeps Player B’s penny; if they do not match, then Player B wins and keeps Player A’s penny.

Matching pennies is a zero-sum game because one player’s gain is the other’s loss. The payoffs for Players A and B are shown in the table below, with the first numeral in cells (a) through (d) representing Player A’s payoff, and the second numeral representing Player B’s playoff. As can be seen, the combined playoff for A and B in all four cells is zero.

Zero-Sum Game Definition in Finance, With Example (2)

How Zero Sum Games Apply to Finance

In the stock market, trading is often thought of as a zero-sum game. However, because trades are made on the basis of future expectations, and traders have different preferences for risk, a trade can be mutually beneficial. Investing longer term is a positive-sum situation because capital flows facilitation production, and jobs that then provide production, and jobs that then provide savings, and income that then provides investment to continue the cycle.

Options and futures trading is the closest practical exampleto a zero-sum game scenario because the contracts are agreements between two parties, and, if one person loses, then the other party gains. While this is a very simplified explanation of options and futures, generally, if the price of that commodity or underlying asset rises (usually against market expectations) within a set time frame, an investor can close the futures contract at a profit. Thus, if an investor makes money from that bet, there will be a corresponding loss, and the net result is a transfer of wealth from one investor to another.

Does Zero-Sum Game Mean All or Nothing?

Yes. Often the terms zero-sum and "all or nothing" are used to describe the same phenomenon: where there can only be one winner, at the expense of the loser(s).

Why Is It Called Zero-Sum?

The term "zero-sum" comes from the fact that some situations require winners to gain at the expense of losers, such that the net value of the system remains unchanged. For example, a winner with +3 would result in, say, two losers, one with -1 and one with -2. The sum is zero (3 - 2 - 1).

What Is a Zero-Sum Game in Relationships?

In the context of personal relationships, a zero-sum game implies that there can only be one "winner" at the expense of the other person or people. This can create conflict and tension.

Zero-Sum Game Definition in Finance, With Example (2024)

FAQs

Zero-Sum Game Definition in Finance, With Example? ›

The term "zero-sum" comes from the fact that some situations require winners to gain at the expense of losers, such that the net value of the system remains unchanged. For example, a winner with +3 would result in, say, two losers, one with -1 and one with -2. The sum is zero (3 - 2 - 1).

What are examples of zero-sum in real life? ›

The board game Monopoly, and the games of chess, bridge, and poker, are all zero-sum game examples. Zero-sum games are also present in economic theories and real-life examples include futures and options trading on the stock market.

What is an example of zero-sum thinking? ›

In a negotiation when one negotiator thinks that they can only gain at the expense of the other party (i.e., that mutual gain is not possible). In the context of social group competition, the belief that more resources for one group (e.g., immigrants) means less for others (e.g., non-immigrants).

Which of the following best describes a zero-sum game? ›

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.

What is an example of a zero-sum negotiation? ›

It is a zero sum game in which one person's gains always come at the expense of another. Bargaining over the price of a product or service is an example in which every dollar advantage you gain by getting the price lowered, the other party loses by receiving one dollar less.

What is a zero-sum game simple example? ›

Poker and gambling are popular examples of zero-sum games since the sum of the amounts won by some players equals the combined losses of the others. Games like chess and tennis, where there is one winner and one loser, are also zero-sum games.

What is a zero-sum game also known as? ›

A zero-sum game is also called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium.

What does it mean when someone says life is a zero-sum game? ›

A zero-sum game is one in which, for any player to improve their outcome, another player's outcome must get worse. In other words, any gains have to be taken from someone else.

Does zero-sum game mean no one wins? ›

Zero-Sum Games. A zero-sum game is one in which no wealth is created or destroyed. So, in a two-player zero-sum game, whatever one player wins, the other loses. Therefore, the player share no common interests.

What is a zero-sum situation also known as? ›

In distributive negotiation, parties compete over the distribution of a fixed pool of value. Here, any gain by one party represents a loss to the other. You may also hear this referred to as a zero-sum negotiation or win-lose negotiation.

What is another name for a zero-sum game? ›

winner-take-all. hard-line. high-stake. win-or-lose. high stakes.

What is an example of a two person zero-sum game? ›

Tic-tac-toe is a simpler example of a two-player zero-sum game. To a game theorist, a strategy for the first player describes the first move and where to move on future opportunities under all possible circ*mstance. This leads to an enormous number of strategies.

Is money a zero-sum game? ›

Thus, most economic activity cannot be called zero-sum games. Still, it is possible for some people to suffer losses. For example, many manufacturing jobs have moved from wealthy countries such as the United States to developing countries, leaving many U.S. workers without jobs, at least temporarily.

What is another name for a zero-sum situation? ›

Since the distribution approach specifies an approach in which one party gains a specific amount if another party losses that amount. So, a Zero-sum situation is also known by another name which is called distributive. Therefore, A Zero-sum situation is also known by another name which is called distributive.

What is the zero-sum rule? ›

Zero-sum rule: The sum of all charges(positive and negative) of all ions in the chemical formula of a compound must be zero.

What is zero sum bias in real life examples? ›

Another example of the zero-sum bias is a child mistakenly believing that their parents' love toward them must come at the expense of their parents' love toward the child's siblings (and vice versa), even if this isn't the case, unlike with some other parental resources, such as time and attention.

What is an example of a zero-sum relationship? ›

A “zero-sum” game is one where any gain that you might make is a loss for your partner. Chess is a perfect example of zero-sum. Gains are shared in a solid business relationship. A construction project could fall into that category, as could a joint venture.

What is the zero-sum game in life? ›

Life is indeed a zero-sum game. Whatever matter comes to a living being from the environment inexorably goes back to the environment. The food that we eat, the water that we drink and even the air that we breathe are returned to the environment.

Is basketball a zero-sum game? ›

Basketball is a great example of a zero-sum game (a game in which both teams pursue the same result, in this case to win). One situation that is easy to analyze is the foul trouble dilemma associated with stars.

Is Rock Paper Scissors a zero-sum game? ›

A rock beats scissors, scissors beat paper by cutting it, and paper beats rock by covering it. In this simulation, the computer has two different strategies that it can follow. Rock, paper, scissors is an example of a zero-sum game without perfect information. Whenever one player wins, the other loses.

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