In this game, q=3/7 means that Player 2 chooses their pure strategy Right (R) with a probability of 3/7, and consequently chooses their pure strategy Left (L) with a probability of 4/7. At this specific mixture, Player 1 is completely indifferent between choosing R and L, receiving an expected payoff of 12/7 regardless of their choice.
Conditions: The game is the displayed 2x2 normal-form game.; Player 2 mixes between R and L with probabilities q and 1−q.; The equilibrium concept is mixed-strategy Nash equilibrium.
In this game, q=3/7 means that Player 2 chooses their pure strategy Right (R) with a probability of 3/7, and consequently chooses their pure strategy Left (L) with a probability of 4/7. At this specific mixture, Player 1 is completely indifferent between choosing R and L, receiving an expected payoff of 12/7 regardless of their choice.
Conditions: The game is the displayed 2x2 normal-form game.; Player 2 mixes between R and L with probabilities q and 1−q.; The equilibrium concept is mixed-strategy Nash equilibrium.
To find Player 2's mixing probability q, you must choose q so that Player 1 is indifferent between their pure strategies, Right (R) and Left (L). This involves computing Player 1's expected payoff from each pure row strategy under Player 2's mixture, setting those two expected payoffs equal to each other, and solving the resulting linear equation for q.
Conditions: Player 2 mixes between R and L with probabilities q and 1−q.; The target player (Player 1) must be made indifferent between the pure strategies being mixed.; The solution for q should lie in [0,1] to represent a valid mixed strategy.
To find Player 2's mixing probability q, you must choose q so that Player 1 is indifferent between their pure strategies, Right (R) and Left (L). This involves computing Player 1's expected payoff from each pure row strategy under Player 2's mixture, setting those two expected payoffs equal to each other, and solving the resulting linear equation for q.
Conditions: Player 2 mixes between R and L with probabilities q and 1−q.; The target player (Player 1) must be made indifferent between the pure strategies being mixed.; The solution for q should lie in [0,1] to represent a valid mixed strategy.