Suppose two companies undertake a joint project. The revenue from the project will be

shared equally between them. Each company's strategy is to choose its effort level

which is represented by $e_i$AAi$=1,2.$ The revenue from the project depends on the total

effort that both companies provide and given by $R(E)=120E-2E^2$ where $E=e_1+e_2$

is the total effort level. Also, the effort is costly; the cost of effort is $e^2$ for company $1$

and $2e^2$ for company $2.$

a$)(5$ p$.)$ Find the payoff functions for both companies

b$)(8$ p$.)$ Find the best response functions for both companies

c$)(7$ p$.)$ Find the Nash Equilibrium of the game