Question

19. [3 Marks] Yifei and Iris each decides whether to attend a party without knowing the choice of the other. A player’s payoff is 0 if she does not attend. If a player attends, her payoff depends on the other’s choice: +5 if the other attends and -5 if the other does not. Which of the following is true?

A. Attending is a dominant strategy.
B. There is no Nash equilibrium of this game.
C. The outcome maximizing the sum of payoffs is not an equilibrium.

D. There are multiple Nash equilibria of this game.

E. None of the above are true.

[The answer is D, Hope to get a detailed explanation,thanks]

Answer 1

Option (D).

Payoff matrix is as follows.

		YiFei
		Attend	Not Attend
Iris	Attend	(5, 5)	(-5, 0)
	Not Attend	(0, -5)	(0, 0)

When YiFei chooses Attend, Iris's best strategy is Attend since payoff is higher (5 > 0).

When YiFei chooses Not Attend, Iris's best strategy is Not Attend since payoff is higher (0 > - 5).

When Iris chooses Attend, YiFei's best strategy is Attend since payoff is higher (5 > 0).

When Iris chooses Not Attend, YiFei's best strategy is Not Attend since payoff is higher (0 > - 5).

So, there are 2 Nash equilibria: (Attend, Attend) and (Not Attend, Not Attend) [see below].

YiFei Attend Not Attend (5 5) (-5, 0) Attend Iris (0 0) (0, -5) Not Attend