I have attached the question and the solution to the answer. I am not sure how to get to the solution, I think I may have to set up a simultaneous game? Can someone please explain?

1. [10 pts] Betty is looking for a job. She considers job opportunities in two cities. Betty's utility is given by y-, where y is the lifetime income and r is the amount spent on buying a house. The income from City 1 fluctuates although the house price is stable. On the contrary, the income from City 2 is stable while the house price fluctuates. If she moves to City 1, Betty can earn a lifetime income y1 with probability o and 1 + y1 with probability 1 - a. The house price in City 1 is m1. Moving to City 2 means that Betty can earn an income of #2. However, the house price is a, with probability y and 1 + 12 with probability 1 - y. Do the following: (@) Write down the expected utilities associated with living in the two respective cities, i.e., V1 and V2. (b) Derive the condition under which Betty chooses City 1.