Question

1. Consider the following game with players Alice and Bob with strategies C and D. What is the solution of this game by iterated strict dominance? Please describe your step.

Table 1: A Game  

Bob
Alice		C	D
	C	2,2	0,3
	D	3,0	1,1

2. For the same game, demonstrate that the Bob and Alice both playing C is or is not a Nash equilibrium.

  

Answer 1

1. When Alice choose C, Bob will not choose C (as 2 < 3).
When Alice choose D, Bob will not choose C (as 0 < 1).
So, column C is eliminated as it is strictly dominated by strategy D because C is never chosen by Bob. So, the game can be written as:

	Bob: D
Alice: C	0,3
Alice: D	1,1

Now, given that D choose D, C's best response is D (as 1 > 0).

So, solution of this game by iterated strict dominance is (D, D) or (1,1)

2. Given that Alice choose C, Bob's best response is D (3)
Given that Alice choose D, Bob's best response is D (1).
Given that Bob choose C, Alice's best response is D (3)
Given that Bob choose D, Alice's best response is D (1).
So, Nash equilibrium of the game is (D, D) or (1,1) as best response of both players occur simultaneously when they choose D. Thus, C is not a Nash equilibrium as D is the only Nash Equilibrium.