There are four players each of whom has an initial endowment of $10. Each player has to decided how much of his initial endowment to invest in a public good. Each player I's payoff is given by u(i) = 0.8G + 10 - x(i), where x(i) is player I's contribution to the public good and G = x1 + x2 + x3 + x4 is the amount of the public good that is being provided.
a) What is the dominant strategy for each player?
b) what contribution levels would be efficient (i.e. maximize the sum of the payoffs of the four players)?