Consider a game in which a player has a dominant strategy.
(i) If the game is played sequentially and the player moves first, will he necessarily choose his dominant strategy? Explain.
(ii) If the game is played sequentially and the player moves second, will he necessarily choose his dominant strategy? Explain.
(i) No, a player may not choose his dominant strategy when he moves first in a sequential game. The only payoff from his dominant strategy that is relevant is the one corresponding to the optimal outcome for the second player. Although this payoff is best when the strategy of the second player is fixed and given, it may not be best when compared to all other payoffs in the game. Thus some other strategy may be preferable to the dominant strategy.
(ii) Yes, a player will choose his dominant strategy when he moves second in a sequential game. No matter what strategy the first player chooses, once that strategy has been fixed, the second player's dominant strategy will give him the highest payoff.
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