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A strategy is strictly dominant if, no matter what the other players do, the strategy earns a player a strictly higher payoff than the other. Hence, a method is strictly dominant if it's invariably strictly higher than the other strategy, for any profile of different players' actions. If a player contains a strictly dominant strategy, than he or she's going to invariably play it in equilibrium. Also, if one strategy is strictly dominant, than all others are dominated. for instance, within the prisoner's dilemma, every player contains a strictly dominant strategy.
1. This question and the next is based on the following description. Consider the coalitional game (referred to as Game 1) given by: N = {1,2,3,4}; v(N) = 3, v{i} = 0, i = 1,...,4,
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