Problem 2: [20 pts + 10 extra] The owner of a rm needs to decide how much to invest to improve its production process. More investment means that the workers are more efcient in generating revenue but is costly. The following game models this investment decision. The timing of the game is as follows: The game begins with the owner, player 1, choosing an investment level a :_> 0. Two employers, player 2 and 3, who work for the owner observe the chosen investment or, and subsequently decide simultaneously on effort levels, ea, 33 2 0. After the invatrnent and efforts have been decided, revenue for the rm is generated according to the following function: 1r(o:, 82,63) = nee: + 133 + 8263. Notice that the higher or is, the more efcient the workers are at converting effort into revenue. Revenue is shared among the three parties in the following way: ,8 E [0,11 proportion of the revenue accrues to the owner while the remaining revenue is split among the workers equally so that each worker obtains ill ,3] proportion of the revenue. Both investment and effort are costly. The owner incurs a cost of o3 for investment (1 while each worker t' incurs a oost of e? by exerting effort 9;. Therefore, the utility functions of the players of this game are as follows: 3 H1(Q, 2! 83) = ling? 'l" 0'33 + 6283) CE 5 l 3 1 ugh}, 6:2, as) = Thurs: + area + 12233} leg. 1 1 Rafe 62. E3) = 2 $0382 + ores + 8293} - 18?;- Part a: {5 pts] Describe the strategies of each of the players in this extensive form game. Part b: .5 pie] Suppose that ,8 = 1/2. Solve for the NE of the simultaneous move in the proper suhgame after the manager has already chcsen the investment level to be or. (Your solution should be written in terms of or} Part c: [I0 ptsf Suppose that ,8 = 1X2. Using your answer to part bT solve for the SPNE of this game. What is the SPNE strategy prole? What is the SPNE outcome? 'What are the payoffs to each of the players in the SPNE'? Port d: fErtm Gratin + 10 ptsj' Solve for the unique SPNE for any ,5 > D. What happens to the manager's profits as ,6 increases? Ebcplain intuitively