Question

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

		Player 2
	Strategy	X	Y
Player 1	A	5, 5	0, -200
	B	-200, 0	20, 20

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

Instructions: You may select more than one answer. Click the box with a check mark for the correct answers and click twice to empty the box for the wrong answers. You must click to select or deselect each option in order to receive full credit.

___	(0,-200)
___	(-200,0)
___	(20,20)
___	(5,5)

Which of these outcomes would you consider most likely?

___	(5,5)
___	(20,20)
___	(-200,0)
___	(0,-200)

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?

Choose B or A


What outcome do you think would occur as a result?

___	(20,20)
___	(-200,0)
___	(5,5)
___	(0,-200)

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?

___	(-200,0)
___	(0,-200)
___	(20,20)
___	(5,5)

Answer 1

a) the nash equilibrium in the above payoffs are option c and d.

The (5,5) equilibrium would seem most likely since the other equilibrium involves some risk if the players do not coordinate on the same equilibrium and it is also the secure strategy for both the players which they can play.

b) If player 1 is permitted to communicate by uttering one syllable before the players simultaneously and independently make their decisions then this would send a signal to the player 2 that player 1 is going to use strategy B, so it would permit the players to coordinate and choose the equilibrium (20,,20)

c) If player 2 can choose its strategy before player 1,player 1 observes player 2 choice before making her decision and this move strategy is known by both players then, Player 2 would choose Y and player 1 will follow by choosing B. This will result in the subgame perfect equilibrium with outcome (20,20).