Question

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

		Player 2
	Strategy	X	Y
Player 1	A	48, 48	-60, 8
	B	8, -60	32, 32

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.

• (-60,8)
• (8,-60)
• (48,48)
• (32,32)

Which of these outcomes would you consider most likely?

• (-60,8)

• (48,48)

• (32,32)

• (8,-60)

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?

• (48,48)

• (-60,8)

• (32,32)

• (8,-60)

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?

• (48,48)

• (32,32)

• (8,-60)

• (-60,8)

Answer 1

A) option C , D

(48,48)

(32,32)

	X	Y
A	(48*,48•)	(-60,8)
B	(8,-60)	(32*,32•)

2) likely outcome (48,48)

3) A)

communicate that he will play A, so that other player also plays A

4) (48,48)

Both will co-operate to earn higher payoff

5) (48,48)

If P2 moves first , he will play X or Y

If he plays X, then P1 will play A

If he plays Y, P1 will play B

Now solving backwards

P2 will play X, as gets higher payoff