Suppose Anne and Bob are partners in a firm and make a continuous effort choice. The total revenue the partnership generates is increasing in the effort of the two partners, but each partner receives disutility from exerting effort. That is, the utility of partner i{A,B} if the effort levels of Anne and Bob are eA and eB is

ui(eA,eB)=3log(1+eA+eB)ei

1. For any effort that Bob could be exerting, determine the effort level Anne would exert to maximize her own utility.
2. For any effort that Anne could be exerting, determin the effort level Bob would exert to maximize his own utility.
3. Does this game have a dominant strategy equilibrium?
4. In light of your answers in parts (1) and (2), for which effort level e* is eA=eB=e a Nash Equilibrium?
5. Suppose that both partners could commit to exert the same level of effort e**. What effort level e** would maximize the utility of each partner?
6. Explain the relations between your answers to parts (4) and (5)