Use the following payoff matrix for a one-shot game to answer the accompanying q

Question

Use the following payoff matrix for a one-shot game to answer the accompanying questions.

a. Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication.

Instructions: In order to receive full credit, you must make a selection for each option. For correct answer(s), click the box once to place a check mark. For incorrect answer(s), click twice to empty the box.

(32,32)unanswered

(4,-25)unanswered

(-25,4)unanswered

(40,40)unchecked

Which of these outcomes would you consider most likely?

(4,-25)

(-25,4)

(32,32)

(40,40)

b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter?

A

B

What outcome do you think would occur as a result?

(-25,4)

(40,40)

(4,-25)

(32,32)

c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is known by both players. What outcome would you expect?

(40,40)

(-25,4)

(32,32)

(4,-25)

Explanation / Answer

Ans a)

We have 2 Nash Equilibrium in this case (A,X ) & (B,Y) that is (32,32) & (40,40)

Ans b)

We need to find Mixed strategy Nash Equilibrium

32q+4(1-q)=-25q+40(1-q)

57q=36(1-q)

q=36/93=12/31

and

p=12/31 hence 1-q=19/31 and 1-p=19/31 then we can vagualy say that possible ouotcome is (B,Y)=(40,40)

Ans b)

Player 1 will always utter B hence possible outcome is (40,40)

Ans c)

Again (40,40) is the answer

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