Question

Question 3: [5pt total] Consider the following game: Player 1 Player 2 X Y Z A 4,0 -3,8 -7, -1 B-4,3 0,6 9,5 C3,2 2,-1 11, 9 Let B1(-) and B2(-) be the best response function for player 1 and player 2 respectively. Calculate the following: 3)a) [1pt] B1(X) 3)b) [1pt] B2(B) 3)c) (1pt] Social Welfare Maximum: 3)d) [1pt] Dominant Strategies for Player 1: 3)) [1pt] Pure Nash Equilibriums:

Answer 1

1. For player 1, if player 2 plays X, the best response is to play A with the maximum payoff of 4

2. For player 2, if player 1 plays B, the best response is to play Y with the maximum payoff of 6

3.  Social welfare maximum:

This is the condition when the total payoffs for Player 1 and 2 is maximum which is the case

when Player 1 plays C and Player 2 plays Z with total payoff of 20

4. Dominant strategies for Player 1

For player 1, one dominant strategy is to play C over B since the payoff is always higher than that of playing B

5. For nash equilibrium

When Player 2 plays X, 1 plays A, when player 2 plays Y, 1 plays C, when plays 2 player Z, 1 plays C

When player 1 plays A, 2 plays Y, when player 1 plays B, 2 plays Y, when player 1 plays C, 2 plays Z

The plays by player 1 and 2 are highlighted in bold below:

		Player 2
		X	Y	Z
	A	4,0	-3,8	-7,-1
Player 1	B	-4,3	0,6	9,5
	C	3,2	2,-1	11,9

As can be seeon on the case C,Z has both bolds that implies this being the nash equilibrium