Payoff Comparison
One strategy dominates another if its payoff is always higher.
Formula
Variables
Example
A dominant strategy is best no matter what the opponent does.
How it works
The symbol a \succ b means that strategy a is strictly preferred to strategy b because its utility is higher: u(a) > u(b). In game theory, this comparison is used to rank options by their outcomes, so a strategy that gives a larger payoff in every relevant case can be called better in the dominance sense. It works because utility is the numerical representation of how desirable an outcome is, so comparing utilities directly tells you which strategy should be chosen.
When to use it
Use this when comparing two strategies, actions, or outcomes in a payoff table or utility model. It is especially useful in dominance analysis, decision-making under uncertainty, and any situation where you need to determine which option is strictly better.
Worked example, step by step
Suppose Player 1 is choosing between two strategies with utilities: Strategy A: u(A) = 18 Strategy B: u(B) = 12 Step 1: Compare the utilities: 18 > 12 Step 2: Write the dominance relation: A \succ B Step 3: Interpret the result: Strategy A is preferred because it gives the higher payoff.
Common mistakes to avoid
- Treating a \succ b as meaning the strategies are equal or only weakly better
- Comparing labels or names of strategies instead of their utility values
- Forgetting that the comparison depends on the chosen utility scale and the relevant payoffs
Did You Know?
In the Prisoner's Dilemma, defecting dominates — yet both players end up worse than if they'd cooperated.
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