Dominant Strategies

Game Theory · Axiom Academy

Unit 2: Dominance and Nash Equilibrium A strategy is strictly dominant if it provides a strictly higher payoff than any alternative strategy, regardless of what the opponent does. Strategy s i strictly dominates strategy s' i if the payoff from s i is always greater than the payoff from s' i , no matter what strategies the other players choose. Watch as we compare payoffs across all opponent choices to identify strict dominance: A strategy is weakly dominant if it provides a payoff at least as good as any alternative strategy for all opponent choices, and strictly better for at least one opponent choice. Strategy s i weakly dominates strategy s' i if the payoff from s i is greater than or equal to the payoff from s' i for all opponent strategies, with strict inequality for at least one. Notice how weak dominance allows for ties in some cases, but requires at least one strict improvement: We can express dominance relationships precisely using mathematical notation, where u i represents player i's utility function and s -i represents the strategies of all other players. Strategy s i strictly dominates s' i if: Strategy s i weakly dominates s' i if: Watch as we visualize how these inequalities work in a payoff matrix:

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