# Zero-Sum Game

#### Quick Summary of Zero-Sum Game

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant’s gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants.

### What is the dictionary definition of Zero-Sum Game?

#### Dictionary Definition

A game in which the sum of the pay-offs to players is zero for every outcome.

In a non-competitive two-player zero-sum game a positive pay-off for one player implies a negative pay-off (of equal value) for the other player.

Zero-sum games represent direct opposition between the interests of the players and examples are often used to method to model conflict.

#### Full Definition of Zero-Sum Game

In mathematical game theory, a zero-sum game is a game in which losses of some of the players are exactly offset by gains of other players.

Chess, for instance, is a zero-sum game, because a win for one player is a loss for another. Since the theory of a zero-sum game has some straightforward implications, one of the first questions an economist will consider in analyzing a market is whether it should be modelled as a zero-sum game or not. Very few business activities resemble a zero-sum game. More typically, each side mutually benefits from an exchange. The stock market is sometimes mistaken for a zero-sum game since one player’s payment to buy shares is exactly matched by the other player’s payment received for selling. The stock market is far from a zero-sum game; substantial wealth is created. To be a zero-sum game, all stocks would have to eventually revert back to the price at which they started trading. In contrast, the futures market is recognized as a zero-sum game.

• A zero-sum game is one in which if one party loses, the other party gains, and the net wealth shift is zero.
• Zero-sum games might have as few as two players or as many as millions.
• Futures and options are considered zero-sum games in financial markets since the contracts represent agreements between two parties and, if one investor loses, the money is transferred to another investment.

According to game theory, the game of matching pennies is a good illustration of a zero-sum game. The game includes two players, A and B, laying a penny on the table at the same time. Whether or not the pennies match determines the payout. Player A wins and keeps Player B’s penny if both pennies are heads or tails; if they don’t match, Player B wins and keeps Player A’s penny.

Because one player’s gain is the other’s loss, matching pennies is a zero-sum game.

Win-win scenarios, such as a trade pact that dramatically improves trade between two countries, or lose-lose events, such as war, are the polar opposites of zero-sum games. However, in real life, things aren’t always that clear, and gains and losses might be tough to calculate.

Trading in the stock market is frequently regarded as a zero-sum game. Because trades are conducted based on future expectations and traders have varying risk preferences, a trade might be mutually advantageous. Longer-term investing is a win-win situation because capital flows facilitate production, which in turn facilitates jobs, which in turn facilitate production, which in turn facilitates jobs, which in turn facilitate savings, which in turn facilitates investment to continue the cycle.

## Zero-Sum Game vs. Game Theory

In economics, game theory is a sophisticated theoretical topic. The basic source is John von Neumann’s landmark 1944 work “Theory of Games and Economic Behavior,” co-authored by Oskar Morgenstern and written by Hungarian-born American mathematician John von Neumann. The study of the decision-making process between two or more intelligent and rational parties is known as game theory.

Experimental economics, which conducts experiments in a controlled context to test economic theories with more real-world understanding, applies game theory in a variety of economic sectors, including experimental economics. When applied to economics, game theory employs mathematical formulae and equations to forecast transaction outcomes while accounting for a variety of variables such as gains, losses, optimality, and individual behaviour.

In theory, a zero-sum game can be solved in three ways, the most famous of which being John Nash’s Nash Equilibrium, which he proposed in a 1951 paper titled “Non-Cooperative Games.” Given knowledge of each other’s choices and the fact that changing their option will not benefit them, the Nash equilibrium states that two or more opponents in the game will not vary from their choice.

## Examples of Zero-Sum Games

When it comes to understanding a zero-sum game in economics, there are several aspects to consider. In a zero-sum game, perfect competition and perfect information are assumed; both opponents in the model have all of the knowledge they need to make an informed decision. After transaction costs, most transactions or trades are fundamentally non-zero-sum games because when two parties agree to trade, they do so with the assumption that the goods or services they will receive are more value than the products or services they would deal for. Most transactions fall into this category, which is known as positive-sum.

Because the contracts are agreements between two parties, and if one party loses, the other party profits, options and futures trading is the closest practical example to a zero-sum game scenario. While this is a highly simple description of options and futures, in general, if the price of that commodity or underlying asset rises (typically against market expectations) within a certain time frame, an investor can profitably close the futures contract. As a result, if an investor profits from that wager, there will be a commensurate loss, resulting in a wealth transfer from one investor to another.

#### Related Phrases

Fair game
Lump sum distribution
Sum of the years' digits depreciation
Zero balance account
Zero beta portfolio
Zero cost collar
Zero coupon bond
Zero curve
Zero growth model
Zero investment portfolio
Zero minus tick
Zero one integer programming
Zero or low coupon bonds
Zero plus tick
Zero prepayment assumption
Zero uptick

#### Zero-Sum Game FAQ's

What is a Zero Sum Game?

A type of game wherein one player can gain only at the expense of another player.

A zero-sum game is a situation in economics where one party’s win causes other parties to lose exactly in the same proportion. The aggregate result of all parties results equals zero.

Zero-Sum Games are described by Game Theory, a field of economics that studies the interaction between participants inside the “game”, a term that describes a given economic scenario. This theory was developed by John von Neumann in his book “Theory of Games and Economic Behavior”. Mathematical models are used to describe the possible outcomes of strategic decisions. One of these “games” are zero-sum games.

These are situations where no value is created, which means that if one of the parties win the other party loses exactly the same amount won by the other side, therefore, the overall result of combining both transactions is zero. This is the case for penny flipping. If two parties bet \$1 in a coin-flipping game and one party picks heads while the other picks tails, the game is a zero-sum game. The result of the coin flip will add \$1 to one of the parties while the other one will lose \$1 as a result.

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#### Definition Sources

Definitions for Zero-Sum Game are sourced/syndicated and enhanced from:

• A Dictionary of Economics (Oxford Quick Reference)
• Oxford Dictionary Of Accounting
• Oxford Dictionary Of Business & Management

This glossary post was last updated: 7th January, 2022 | 0 Views.