L C R U 7,4 0, 3 4, 1 M 6, 1 3, 4 72, 0 D 5,2 -1,86 3, 1 Consider the game below. Let p₁ be the probability Player 1 (the row player) picks U, p2 be the probability Player 1 picks M, q₁ be the probability Player 2 (the column player) picks L, and q2 be the probability Player 2 (the column player) picks M. Find all the pure strategy and mixed strategy Nash equilibria, if any. (a) There are two pure strategy Nash Equilibrium, one with (U,L) and one with (M,C), and one mixed strategy Nash equilibria with p₁ = 1/4, p2 = 1/4, 91 = 1/2, and q2 = 3/4. (b) There are two pure strategy Nash Equilibrium, one with (D,C) and one with (M,R), and one mixed strategy Nash equilibria with p₁ = 1/4, p2 = 3/4, 91 = 1/2, and 92 = 1/2. (c) There are two pure strategy Nash Equilibrium, one with (6,1) and one with (0,3), and one mixed strategy Nash equilibria with p₁ = 1/2, p2 = 1/4, 91 = 1/7, and 92 = 3/4. (d) There are two pure strategy Nash Equilibrium, one with (U,L) and one with (M,C), and one mixed strategy Nash equilibria with p₁ = 3/4, p2 = 1/4, 91 = 3/4, and 92 = 1/4. (e) None of the above.
L C R U 7,4 0, 3 4, 1 M 6, 1 3, 4 72, 0 D 5,2 -1,86 3, 1 Consider the game below. Let p₁ be the probability Player 1 (the row player) picks U, p2 be the probability Player 1 picks M, q₁ be the probability Player 2 (the column player) picks L, and q2 be the probability Player 2 (the column player) picks M. Find all the pure strategy and mixed strategy Nash equilibria, if any. (a) There are two pure strategy Nash Equilibrium, one with (U,L) and one with (M,C), and one mixed strategy Nash equilibria with p₁ = 1/4, p2 = 1/4, 91 = 1/2, and q2 = 3/4. (b) There are two pure strategy Nash Equilibrium, one with (D,C) and one with (M,R), and one mixed strategy Nash equilibria with p₁ = 1/4, p2 = 3/4, 91 = 1/2, and 92 = 1/2. (c) There are two pure strategy Nash Equilibrium, one with (6,1) and one with (0,3), and one mixed strategy Nash equilibria with p₁ = 1/2, p2 = 1/4, 91 = 1/7, and 92 = 3/4. (d) There are two pure strategy Nash Equilibrium, one with (U,L) and one with (M,C), and one mixed strategy Nash equilibria with p₁ = 3/4, p2 = 1/4, 91 = 3/4, and 92 = 1/4. (e) None of the above.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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Transcribed Image Text:L
C
R
U
7, 4
0, 3
4, 1
M
6, 1
3, 4
72, 0
D 5,2 -1,86
3, 1
Consider the game below. Let p₁ be the probability Player 1 (the row player) picks U, p2 be
the probability Player 1 picks M, q₁ be the probability Player 2 (the column player) picks L,
and
92 be the probability Player 2 (the column player) picks M. Find all the pure strategy
and mixed strategy Nash equilibria, if any.
(a) There are two pure strategy Nash Equilibrium, one with (U,L) and one with (M,C), and
one mixed strategy Nash equilibria with p₁ = 1/4, p2 = 1/4, 91 = 1/2, and 92 = 3/4.
(b) There are two pure strategy Nash Equilibrium, one with (D,C) and one with (M,R), and
one mixed strategy Nash equilibria with p₁ = 1/4, p2 = 3/4, 91 = 1/2, and 92 = 1/2.
(c) There are two pure strategy Nash Equilibrium, one with (6,1) and one with (0,3), and
one mixed strategy Nash equilibria with pi = 1/2, p2 = 1/4, 91 = 1/7, and 92 = 3/4.
(d) There are two pure strategy Nash Equilibrium, one with (U,L) and one with (M,C), and
one mixed strategy Nash equilibria with p₁ = 3/4, p2 = 1/4, 91 = 3/4, and 92 = 1/4.
(e) None of the above.
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