Game Theory & Decision

Intermediate

Payoff Comparison

One strategy dominates another if its payoff is always higher.

Formula

a \succ b \iff u(a) > u(b)

Variables

u(a)Utility of strategy a

u(b)Utility of strategy b

Example

A dominant strategy is best no matter what the opponent does.

Did You Know?

In the Prisoner's Dilemma, defecting dominates — yet both players end up worse than if they'd cooperated.

game theory dominance strategy

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Expected Value

Probability-weighted average outcome of a decision.

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Optimal fraction of bankroll to bet for long-run growth.

Expected Utility

Weighted average of the utility of outcomes, not just their cash value.

Minimax Value

Best worst-case payoff a player can guarantee.

Mixed Strategy (Indifference)

Probability that makes an opponent indifferent between their options.

Bayes' Theorem

Update a belief's probability given new evidence.