ofstionConsider the payoff matrix M for a non-zero-sum game between player 1 with a choice of moves d₁ and d₂, andplayer 2 with a choice of moves 8₁ and 82. The payoffs are given in the following matrix M:81 82d₁ (4,8) (2,0)d₂ (6,2) (0,8)What is the Nash equilibrium?O a. There is a mixed-strategy Nash equilibrium: x* =O b. There is no Nash equilibriumO C.O d.O e.d2, 81Of. d1, 82O g. d2, 82O h.d₁, 81O i.O j.112' 2'There is a mixed-strategy Nash equilibrium: x*3 4There is a mixed-strategy Nash equilibrium: x* = ₁, y =3 4tch-t*עיד יד||4יד יד1 122 24 3من الـ4 331,717,0* = 7,477There is a mixed-strategy Nash equilibrium: x*There is a mixed-strategy Nash equilibrium: * = 1, y = 1, 12'2' 2 We consider a coalitional game with 3 players A, B, C. If the 3 players form a grand coalition, what is the fairpayoff division or Shapley value x, knowing that:v({1}) = 6, v({2}) = 0, v({3}) = 6,;v({1, 2}) = 42, v({1, 3}) = 24, v({2, 3}) = 18;v({1, 2, 3]) = 72?[Some of the proposed answers should never be considered, and eliminated immediately. Chosing them will result innegative grading, -1. Other wrong answers, but not obviously wrong, will get you O. Leaving it blank: 0. Full marks: 2.]O a. x = (30, 20, 22)(32, 24, 20)O b. x =O c. x =O d. x =O e.O f.x =(30, 24, 18)O g.Oh. x =(24, 22, 20)(42, 24, 18)x = (32, 22, 18)x = (24, 24, 24)(36,0, 36)

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Consider the payoff matrix M for a non-zero-sum game between player 1 with a choice of moves d₁ and do, and player 2 with a choice of moves 6₁ and 82. The payoffs are given in the following matrix M: 81 82 d₁ (4,8) (2,0) d₂ (6,2) (0,8) What is the Nash equilibrium?

Consider the payoff matrix M for a non-zero-sum game between player 1 with a choice of moves d₁ and do, and player 2 with a choice of moves 6₁ and 82. The payoffs are given in the following matrix M: 81 82 d₁ (4,8) (2,0) d₂ (6,2) (0,8) What is the Nash equilibrium?

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Question

of
stion
Consider the payoff matrix M for a non-zero-sum game between player 1 with a choice of moves d₁ and d₂, and
player 2 with a choice of moves 8₁ and 82. The payoffs are given in the following matrix M:
81 82
d₁ (4,8) (2,0)
d₂ (6,2) (0,8)
What is the Nash equilibrium?
O a. There is a mixed-strategy Nash equilibrium: x* =
O b. There is no Nash equilibrium
O C.
O d.
O e.
d2, 81
Of. d1, 82
O g. d2, 82
O h.
d₁, 81
O i.
O j.
11
2' 2'
There is a mixed-strategy Nash equilibrium: x*
3 4
There is a mixed-strategy Nash equilibrium: x* = ₁, y =
3 4
tch-t
*עיד יד
||
4
יד יד
1 1
22 2
4 3
من الـ
4 3
3
1,717,0* = 7,4
77
There is a mixed-strategy Nash equilibrium: x*
There is a mixed-strategy Nash equilibrium: * = 1, y = 1, 1
2'
2' 2

We consider a coalitional game with 3 players A, B, C. If the 3 players form a grand coalition, what is the fair
payoff division or Shapley value x, knowing that:
v({1}) = 6, v({2}) = 0, v({3}) = 6,;
v({1, 2}) = 42, v({1, 3}) = 24, v({2, 3}) = 18;
v({1, 2, 3]) = 72?
[Some of the proposed answers should never be considered, and eliminated immediately. Chosing them will result in
negative grading, -1. Other wrong answers, but not obviously wrong, will get you O. Leaving it blank: 0. Full marks: 2.]
O a. x = (30, 20, 22)
(32, 24, 20)
O b. x =
O c. x =
O d. x =
O e.
O f.
x =
(30, 24, 18)
O g.
Oh. x =
(24, 22, 20)
(42, 24, 18)
x = (32, 22, 18)
x = (24, 24, 24)
(36,0, 36)

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