Question: Consider a two-player game with pure-strategy sets S1 = {1, . . . , m} and S2 = {1, . . . , n}, and

Consider a two-player game with pure-strategy sets S1 = {1, . . . , m} and S2 = {1, . . . , n}, and let (1, 2) be a strategy profile where 1 = (p1, . . . , pm). If 1 is a best response for player 1 against 2, and if p1 > 0 and p2 > 0, then each of 1 and 2 must also be best responses for player 1 against 2. Why?

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