Iterated Dominance

Game Theory · Axiom Academy

Unit 2 - Dominance and Nash Equilibrium Iterated elimination of dominated strategies follows a simple but powerful algorithm: Step 1: Identify and eliminate any strictly dominated strategies Step 2: Look at the reduced game (with eliminated strategies removed) Step 3: Check if any new dominated strategies have emerged Step 4: Repeat until no more dominated strategies exist The key insight is that removing dominated strategies can create new dominance relationships that weren't visible in the original game. A rational player will never play a dominated strategy. Since all players know this, they can safely assume dominated strategies won't be played. This allows us to analyze the simpler, reduced game. Let's work through a concrete example to see how multiple rounds of elimination reveal a solution: Consider a 3x3 game between Player 1 (rows) and Player 2 (columns). The animation shows how strategies are eliminated one round at a time. Round 1: Player 1's Bottom strategy is strictly dominated by Middle (3 > 2, 4 > 3). Eliminate Bottom. Round 2: In the reduced 2x3 game, Player 2's Right strategy is now dominated by Center (3 > 2 for Top, 4 > 3 for Middle). Eliminate Right. Round 3: Player 1's Top is dominated by Middle (4 > 3, 5 > 4). Eliminate Top. Result: The unique solution is (Middle, Center) with payoff (4, 5).

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