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Answers for “为什么在求解对手的混合策略时我们要将两个期望收益设为相等?”

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In this game, q=3/7q = 3/7 means that Player 2 chooses their pure strategy Right (R) with a probability of 3/73/7, and consequently chooses their pure strategy Left (L) with a probability of 4/74/7. At this specific mixture, Player 1 is completely indifferent between choosing R and L, receiving an expected payoff of 12/712/7 regardless of their choice.

Conditions: The game is the displayed 2x2 normal-form game.; Player 2 mixes between R and L with probabilities qq and 1−q1-q.; The equilibrium concept is mixed-strategy Nash equilibrium.