In the following game, in which s1 = (p, 1 − p) is Player 1’s strategy and s2 = (q, 1 − q) isPlayer 2’s strategy, Player 2 is indifferent between L and R when p is equal to: [Write you answeras a decimal number, e.g. 0.33]q 1 − qL Rp U 0, 0 3,31 − p D 1, 1 0,0
Question
In the following game, in which s1 = (p, 1 − p) is Player 1’s strategy and s2 = (q, 1 − q) isPlayer 2’s strategy, Player 2 is indifferent between L and R when p is equal to: [Write you answeras a decimal number, e.g. 0.33]q 1 − qL Rp U 0, 0 3,31 − p D 1, 1 0,0
Solution
The game you're referring to is a type of simultaneous move game often analyzed in game theory. In this game, each player has two strategies. Player 1 can choose U (up) or D (down), and Player 2 can choose L (left) or R (right). The payoffs for each player are given in the matrix.
Player 2 is indifferent between choosing L and R when the expected payoff from both strategies is the same. We can find the value of p that makes Player 2 indifferent by setting the expected payoffs equal to each other and solving for p.
The expected payoff from choosing L is: q*(0) + (1-q)(1) = 1 - q The expected payoff from choosing R is: p(3) + (1-p)*(0) = 3p
Setting these equal to each other gives us the equation: 1 - q = 3p
Solving this equation for p gives us: p = (1 - q) / 3
So, Player 2 is indifferent between choosing L and R when p is equal to (1 - q) / 3.
Similar Questions
In the following game, in which s1 = (p, 1 − p) is Player 1’s strategy and s2 = (q, 1 − q) isPlayer 2’s strategy, Player 1 is indifferent between U and D when q is equal to
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