Problem 4: [30 [1115] Consider the following dynamic game between two workers at a firm. The game begins with worker I who decides on an effort level e1. Worker 2 then observes the effort level of worker 1, el, and then decides what effort, 2, to provide. Assume that when efforts el and 2 are chem by the workers, the worker together generate revenue: :rrlIehe = eel + le; + eleg. The revenue is shared equally among the two workers while each worker incurs a cost from exerting effort. Therefore, each worker obtains the following respective utilities in this game: 1 1 \"1(31'32] = E [gel + es + we) ' Est. 1 1 2 2(31,32] = E [0531 + .632 + 3162) E2_ Part a: [16' pie,Ir Suppose that o: = = 1. Solve for the subgame perfect Nash equilibrium {SFNE} of this game. What is the SPNE outcome of this game? 1What are the payoffs of each player in the SPNE? What is the revenue generated by the rm in the SPNE? Part :5: [15' ptsf Now suppose that o.- = ,5 = 1, but that the workers decide the effort levels simultaneously. Suppose that the utility functions are unchanged. 'What is the resulting Nash equilibrium of this game? What are the payoffs in NE for each player? What is the revenue generated by the rm in the NE? Part c: {I If} grits}r Now suppose that 11,;3 can be any positive real number. Solve for the SPNE of the original dynamic game in which worker 1 decides rst his!\" her effort level followed by worker 2.1 How much revenue is generated in the SPNE? Part (E: [16' pts Errru Cred-it} Suppose you have been hired to manage the rm. Suppose that or :5- ,8 so that worker I is the more eicient worker. 1ifou can either have worker 1 choose effort rst {and worker 2 observe worker 1's effort before deciding effort}, or you can have worker 2 choom effort rst (and have the worker I observe worker Ts effort before deciding effort}. Which ordering of decisions would you prefer to maximize revenue