Problem 3 (30 points) Consider the strategic-form game depicted below: (a) Does this game have a Nash equilibrium in pure strategies? Explain. Let p1
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(a) denote the probability with which player 1 (the row player) plays strategy a, let p 1
(b) be the probability with which she plays strategy b, and p 1
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(c) be the probability with which she plays strategy c. Let p 2
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(a) be the probability with which player 2 (the column player) plays strategy a and let p 2
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(b) be the probability with which he plays strategy b. (b) Show that there is no mixed-strategy Nash equilibrium where p 1 (a)>0, p 1(b)>0, and p 1
(c)>0. (c) Show that there is no mixed-strategy Nash equilibrium where p 1(a)>0, p 1(b)>0, and p 1(c)=0 (d) Show that there is no mixed-strategy Nash equilibrium where p 1 (a)>0, p 1 (b)=0, and p 1(c)>0. (e) There is a (unique) mixed-strategy Nash equilibrium where p 1 (a)=0, p 1(b)>0, and p 1(c)>0. Compute this equilibrium.