1. Given the following game, answer the questions below (Payoffs are written as (A,B)):
B
Left Center Right
A Up (4,1) (2,0) (3,6)
Middle (1,6) (1,4) (2,2)
Down (3,4) (6,3) (4,3)
a. Determine if the game has any pure strategy Nash Equilibriums.
b. Determine the Nash Equilibrium for Player B if Player A makes his/her choice by randomly choosing Up, Middle or Down.
c. Now explain what happens to your answer in part b. if Player A is known as a person who:
i. Likes to take risks.
ii. Does not like to take risks.
d. Determine the Nash Equilibrium if the game was sequential and Player A goes first.