A strategy giving at least as large a payoff as every alternative against every opponent strategy profile. Under the convention distinguishing weak dominance from complete payoff equivalence, require a strict advantage somewhere. In a two-action finite game, it suffices to check the opponent's pure strategies: expected payoff differences against an opponent's mixed strategy are weighted averages of those pure-action comparisons.
A strategy profile in which each player uses a dominant strategy. Every such profile is a Nash equilibrium, since each prescribed choice is a best response to the actual opposing choices in particular. The converse fails: a Nash equilibrium only requires a best response to those actual choices. With the weak convention for dominant strategy, ties are allowed; a strictly dominant strategy requires strict improvement over every alternative against every opposing profile.
A strictly dominant strategy gives a strictly greater payoff than every alternative strategy for every strategy profile of the other players.
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