pr4abc.domin

# pr4abc.domin - Dominance Solvable Games A Introduction...

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Dominance Solvable Games A. Introduction Strict Dominance: defined Preserving dominant strategies and eliminating dominated strategies is a powerful procedure of simplifying games. One strategy is said to (strictly) dominate another if the player in question does (strictly) better with the first than with the second, no matter what other players do. It follows that a (strictly) dominated strategy will never be played by a rational player. It will never be used in any Nash equilibrium. By implication, (strictly) dominated strategies can be eliminated without loss; so, a game can be simplified. This is particularly true of games that have a dominant strategy. Dominant strategy: a single strategy that dominates all other strategies for the same player.

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Example of a Dominated Strategy t 1 Player II t 2 t 3 t 4 s 1 6,3 2,5 1,3 3,2 3,5 2,2 4,5 s 2 5,2 6,4 0,6 s 3 5,0 4,1 3,3 s 4 4,8 1,7 2,6 Player I t 4 is dominated by t 3 (Why?) Example of a Dominant Strategy Player II LCR T 0, 3 2, 2 1, 2.5 M 1, 1 3, 2 2, 1.5 B -1, 2 2, 2 1, 2.5 Player 1 M is a dominant strategy for player I (Why?)
Domination in a two-player game Dominant strategies A pure strategy s*

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pr4abc.domin - Dominance Solvable Games A Introduction...

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