What Is a Zero-Sum Game?

A situation known as zero-sum is one in which the net change in wealth or profit is zero since one person’s gain equals another’s loss. This scenario is often mentioned in game theory. There may be as few as two players in a zero-sum game as millions of players.

The financial markets’ options and futures are zero-sum games when transaction costs are removed. A counter-party always loses a contract for every party that benefits.

Understanding Zero-Sum Games

Zero-sum games occur in a variety of settings. Since the total of the winnings made by some players equals the sum of the losses caused by all other players, poker, and gambling are typical instances of zero-sum games. Zero-sum games include those with a single winner and loser, such as chess and tennis.

Trades in derivatives are often called zero-sum games since one side of the transaction must lose every dollar gained.

Positive Sum vs. Zero Sum Games

Zero-sum games are the antithesis of win-win circumstances, such as a trade pact that significantly boosts commerce between two countries or lose-lose circumstances like a war. But in real life, things are not always clear-cut, and it’s sometimes challenging to put wins and losses into numerical terms.

When interpreting a zero-sum game in the context of economics, there are many things to take into account. A zero-sum game is predicated on the assumption of perfect knowledge and competitiveness, whereby both players in the model possess all the necessary data to make well-informed decisions. When two parties agree to trade, they do so with the idea that, after transaction expenses, the goods or services they are getting are more valuable than the products or services they are dealing for. This means that most transactions or trades are fundamentally non-zero-sum games. This is referred to as the positive sum, and it includes the majority of transactions.

Non-zero sum also applies to well-known game theory instances, such as the Centipede Game, Cournot Competition, Prisoner’s Dilemma, and Deadlock.

Even if there could be some winners and losers, a positive sum game is one in which the net outcome is more significant than zero. Trade and exchange are seen as instances of positive-sum games in economics.

Games with Zero-Sum and Game Theory

An intricate theoretical area of economics research is game theory. The critical 1944 publication “Theory of Games and Economic Behavior,” co-written by Oskar Morgenstern and American mathematician John von Neumann, born in Hungary, is the primary source. The study of decision-making between two or more rational and intelligent actors is known as game theory.

Numerous economic disciplines may benefit from game theory, including experimental economics, which tests economic theories with more practical knowledge via controlled experiments. In economics, game theory employs mathematical formulae and equations to forecast transaction outcomes while accounting for various variables, such as profits, losses, optimality, and human behavior.

There are three theoretically viable solutions to a zero-sum game, the most well-known of which is the Nash equilibrium that John Nash put forth in his 1951 book “Non-Cooperative Games.” According to the Nash equilibrium, if two or more players know each other’s decisions and know there is no gain in altering their own, they won’t change their course of action.

A Zero-Sum Game Example

Game theory sometimes uses the game of matching pennies to illustrate a zero-sum game. In this game, A and B are the players who simultaneously place a penny on the table. Whether or not the pennies match determines the payout. Player A wins and retains Player B’s cent if both pennies are heads or tails; if they don’t check, Player B wins and keeps Player A’s penny.

Matching pennies is a zero-sum game since one player’s gain equals the other’s loss. The table below displays the payoffs for Players A and B. The first numeral in cells (a) through (d) represents Player A’s gain, and the second number represents Player B’s reward. The combined playoff for A and B in all four cells is zero.

Zero Sum Games’ Financial Applications

Trading in the stock market is sometimes seen as a zero-sum endeavor. However, a trade may benefit both parties since it is based on future expectations, and traders have varying tolerances for risk. Long-term investing is a positive-sum game because capital flows support production, which in turn supports jobs that support production and helps savings and investment feed the cycle.

The most realistic illustration of a zero-sum game situation is seen in options and futures trading, where two parties enter into contracts whereby if one loses, the other wins. This is a fundamental explanation of options and futures. Still, generally, an investor may terminate a futures contract profitably if the underlying asset or commodity price increases within a specific window—usually against the market’s expectations. A transfer of wealth from one investor to another will occur if an investor wins money on that wager, and there will also be a corresponding loss.

Does “All or Nothing” apply to zero-sum games?

Sure. The phrases “all or nothing” and “zero sum” are often used to refer to the same situation in which there can only be one winner at the cost of the loser(s).

What Gives It the Name Zero-Sum?

The phrase “zero-sum” refers to circumstances in which victors must profit at the cost of losers to maintain the system’s net worth. A winner with +3, for instance, would produce, let’s say, two losers, one with -1 and one with -2. Three minus two minus 1 equals 0 in total.

What are relationships in a zero-sum game?

A zero-sum game suggests that there can only be one “winner” in human interactions at the cost of the other person or persons. Tension and conflict may result from this.

Conclusion

• 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; if one investor loses, the wealth is transferred to another investor.
• Most transactions are non-zero-sum games because the result can benefit both parties.