Question 1 Consider the following game, where player A has strategies Up and Dow

ID: 1115463 • Letter: Q

Question

Question 1 Consider the following game, where player A has strategies Up and Down, while player B has strategies Left and Right. Player B Strategy Left Up Down Right $2, $2 $4, $8 Player A $5, $3 $3, $6 a) Solve for the Nash equilibrium(s) of this game, and circle the payoff. Do players A or B have a dominant strategy? b) Write out the sequential form of this game, assuming player A moves first. Solve for the subgame perfect equilibrium outcome, and circle the payoff PrtScn Home End Pgt FS F6 F7 FB F9 F4

Explanation / Answer

Player B

STRATEGY

LEFT

RIGHT

Player A

5, 3

2, 2

DOWN

3, 6

4, 8

Nash equilibrium is given by the strategy which is the best response to each other. In our example, the underlined payoff (2,2) is the Nash equilibrium. Hence, UP is a best response strategy for player A to player B playing Right.

To check for Dominant strategy of A and B:

When B is left , if A goes down he gets $3, but if he goes UP then he gets $5, hence player A will go UP when B is Left.

When B is right, if A goes down he gets $4 but if he goes UP he gets $2, hence player A will go Down when B is right.

Hence, Player A has no dominant strategy as its decision to move UP or DOWN is based on the decision of player B.

Now, when A is UP , if b goes left he gets $3, but if he goes right then he gets $2, hence player B will go left when A is UP.

When A is down, if B goes left he gets $6 but if he goes right he gets $8, hence player B will go Right when A is down.

Hence, Player B also has no dominant strategy as its decision to move left or right is based on the decision of player A.