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TL;DR

A probability distribution over pure strategies. Player i plays strategy \( s_j \) with probability \( p_j \), where \( \sum p_j = 1 \). The expected payoff is the probability-weighted average over all strategy combinations.

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

Mixed Strategy

A probability distribution over pure strategies. Player i plays strategy \( s_j \) with probability \( p_j \), where \( \sum p_j = 1 \). The expected payoff is the probability-weighted average over all strategy combinations.

Why it matters for interviews

Many games (matching pennies, rock-paper-scissors) have no pure strategy equilibrium and require mixed strategies. Understanding randomization in competitive settings models bluffing in trading and optimal order routing.

Definition and Mathematical Foundation

A probability distribution over pure strategies. Player i plays strategy \( s_j \) with probability \( p_j \), where \( \sum p_j = 1 \). The expected payoff is the probability-weighted average over all strategy combinations.

Application in Quantitative Finance

Many games (matching pennies, rock-paper-scissors) have no pure strategy equilibrium and require mixed strategies. Understanding randomization in competitive settings models bluffing in trading and optimal order routing.

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Frequently Asked Questions

How do you find mixed strategy equilibria?▼
Each player chooses mixing probabilities to make the opponent indifferent between their pure strategies. Set the opponent's expected payoffs equal across strategies and solve the resulting system.
Why would a rational player randomize?▼
Randomization prevents the opponent from exploiting predictability. In matching pennies, any deterministic strategy is exploitable. The mixed equilibrium is the only unexploitable strategy.
How does mixed strategy theory apply to order execution?▼
Algorithmic traders randomize order timing, sizes, and venue selection to avoid being predictable to adversarial algorithms that detect and front-run deterministic patterns.