TL;DR

A game where one player's gain is exactly another's loss: the payoffs sum to zero. Formally, \( u_1(s) + u_2(s) = 0 \) for all strategy profiles s.

By Valenke Exam Prep Team·Last updated 2026-06-03

Zero-Sum Game

A game where one player's gain is exactly another's loss: the payoffs sum to zero. Formally, \( u_1(s) + u_2(s) = 0 \) for all strategy profiles s.

Why it matters for interviews

Many trading interactions are approximately zero-sum (especially short-term). Understanding zero-sum game theory helps model competitive market dynamics and adversarial selection in order flow.

Definition and Mathematical Foundation

A game where one player's gain is exactly another's loss: the payoffs sum to zero. Formally, \( u_1(s) + u_2(s) = 0 \) for all strategy profiles s.

Application in Quantitative Finance

Many trading interactions are approximately zero-sum (especially short-term). Understanding zero-sum game theory helps model competitive market dynamics and adversarial selection in order flow.

Related Terms

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Frequently Asked Questions

Is the stock market a zero-sum game?▼

Short-term trading is approximately zero-sum (one trader's profit is another's loss, minus transaction costs). Long-term investing is positive-sum because of economic growth and earnings. Options trading is zero-sum between writer and buyer.

How do you solve a 2x2 zero-sum game?▼

Check for saddle points first. If none, use mixed strategies: each player randomizes to make the opponent indifferent. The mixing probabilities are computed from the payoff matrix.

What is the value of a zero-sum game?▼

The expected payoff under optimal play by both sides. By the minimax theorem, this value is unique and equals both the maximin and minimax values.