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20 game theory lecture 2 dominant strategies iterated

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Unformatted text preview: d strategy for both players. No “rational” player would choose “suicide”. Thus if prisoner 1 is certain that prisoner 2 is rational, then he can eliminate the latter’s “suicide” strategy, and likewise for prisoner 2. Thus after one round of elimination of strictly dominated strategies, we are back to the prisoner’s dilemma game, which has a dominant strategy equilibrium. Thus iterated elimination of strictly dominated strategies leads to a unique outcome, “confess, confess”—thus the game is dominance solvable. 20 Game Theory: Lecture 2 Dominant Strategies Iterated Elimination of Strictly Dominated Strategies (continued) More formally, we can follow the following iterative procedure: Step 0: Define, for each i , Si0 = Si . Step 1: Define, for each i , � � � � 0 Si1 = si ∈ Si0 | �si� ∈ Si0 s.t. ui si� , s−i > ui (si , s−i ) ∀ s−i ∈ S−i . ... Step k: Define, for each i , � � � � k Sik = si ∈ Sik −1 | �si� ∈ Sik −1 s.t. ui si� , s−i > ui (si , s−i ) ∀ s−i ∈ S−...
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