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 p₁ = 1/2, p2 = 1/4, 91 = 1/7, and q₂ = 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 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 p₁ = 1/2, p2 = 1/4, 91 = 1/7, and q₂ = 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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Question
**Practice**
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 p₁ = 1/2, p2 = 1/4, 91 = 1/7, and q₂ = 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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