In a game involving two players, Player A has a dominant strategy to choose Action X, while Player B has a mixed strategy involving a probability of playing Action Y. If the payoff matrix indicates that Action X guarantees a payoff of 10 for Player A regardless of Player B's choice, what can be concluded about Player B's optimal strategy?

Because Player A’s dominant action X guarantees a payoff of 10 no matter what Player B does, Player B’s choice cannot improve Player A’s payoff. Player B therefore only cares about its own payoff against A’s inevitable X. Thus B’s optimal strategy is to play whichever action gives B the highest payoff when facing X—if one action dominates, B will play that pure action; if B is indifferent, any mix is fine. For example, if B earns 5 when playing Y against X but 7 when playing Z, B’s best reply is to play Z with probability 1.