Understanding Zero-Sum Games in Finance: Definition and Real-World Example

Gordon Scott has been a dedicated investor and technical analyst for over 20 years and holds the Chartered Market Technician (CMT) designation.

What Exactly Is a Zero-Sum Game?

A zero-sum game describes a scenario where one participant's gain is exactly balanced by another participant's loss, making the overall net benefit zero.

This idea is central to game theory. Classic games like chess perfectly illustrate zero-sum dynamics, where one player's victory directly corresponds to the other's defeat.

In financial markets, certain transactions such as trading options and futures contracts are zero-sum games. Each contract involves two parties; whenever one profits, the other incurs an equal loss.

With millions of participants, financial markets often redistribute wealth without increasing the total sum, embodying the zero-sum principle.

Key Insights

• A zero-sum game concludes with winners and losers but no overall net gain.
• It can involve just two players or millions of participants.
• Futures and options trading exemplify zero-sum games in finance, where one party's gain is another's loss.
• Most real-world transactions are non-zero-sum, benefiting all parties involved.

Delving Deeper Into Zero-Sum Games

Zero-sum games appear in various settings. For instance, poker is zero-sum because the total amount won by some players equals the losses of others; the pot size remains constant.

Competitive games like chess and tennis, where there is a clear winner and loser, also fit this model.

Derivatives trading is frequently cited as zero-sum since every dollar gained by one side comes directly from the other.

Zero-Sum vs. Positive-Sum Games

Zero-sum games contrast with positive-sum scenarios, such as beneficial trade agreements that create value for all parties involved. Conversely, lose-lose outcomes occur when negotiations fail without any party gaining.

In reality, gains and losses can be complex and hard to measure precisely.

Perfect Competition Explained

Economic zero-sum games assume perfect competition and complete information, where all players have access to relevant data to make optimal decisions.

Most trades, however, are positive-sum because both parties expect to gain value exceeding what they give up, after costs.

Examples like the prisoner’s dilemma, Cournot competition, the Centipede game, and Deadlock illustrate non-zero-sum dynamics.

Quick Fact

Positive-sum games yield a net gain greater than zero, even if some participants lose. Trade and exchange are classic examples in economics.

Game Theory and Zero-Sum Games

Game theory, pioneered by John von Neumann and Oskar Morgenstern in 1944, studies strategic decision-making among rational players.

It applies mathematical models to predict outcomes based on players’ choices, gains, and losses.

One key solution concept is Nash Equilibrium, introduced by John Nash in 1951, where players settle on strategies knowing no unilateral change benefits them.

Zero-Sum Game Example: Matching Pennies

Matching pennies involves two players simultaneously placing a penny on the table. If pennies match (both heads or tails), Player A wins Player B’s penny; if not, Player B wins Player A’s penny.

This game perfectly illustrates zero-sum dynamics: one player’s gain is the other's loss. The total payoff sums to zero in all outcomes.

Zero-Sum Games in Financial Markets

Stock market trading is often viewed as zero-sum, but since traders have varied expectations and risk tolerances, trades can be mutually advantageous.

Long-term investing is typically positive-sum, as capital promotes production, employment, and income generation, fueling ongoing investment.

Options and futures trading closely resemble zero-sum games because one party’s gain corresponds to the other’s loss.

For example, if an underlying asset’s price moves favorably within a contract period, the winning investor’s profit equals the losing party’s loss, transferring wealth between them.

Does Zero-Sum Mean All or Nothing?

Yes. The term zero-sum often implies an “all or nothing” outcome where one participant’s gain comes entirely at another’s expense.

Origin of the Term Zero-Sum

The phrase zero-sum reflects that total gains and losses balance out to zero. For instance, a winner gaining +3 points balanced by two losers losing -1 and -2 points results in a net sum of zero.

Zero-Sum Games in Relationships

In personal relationships, zero-sum dynamics suggest one person’s success comes at another’s cost, potentially causing conflict and tension.

Final Thoughts

Zero-sum games involve winners and losers with no net gain overall. Fortunately, most real-life interactions are non-zero-sum, where multiple parties can benefit and the total value created exceeds what is risked.

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