Q2(20): Consider the following public goods game. A group has 4 members. Each group member 1' is endowed with $12 and needs to allocate M: (x: is an integer between 0 and 12) out of the $12 to a public account and $(12 xi) to a private account. The total amount in the public account is the summation of the money allocated by all group members. Each dollar from the public account gives 40 cents (0.4$) as a return to each group member, and each dollar om the private account gives a return of 80 cents (08$) to the group member who owns it. The payoff for each player is the total payoff from the public account and the private account. a) Specify what are the players, strategies, and the payoffs of the game. Write down the payoff as a function of xi. b) Solve all of the pure-strategy Nash equilibria. c) What is the efcient outcome of the game? Is it one of the equilibrium outcome(s)'? If not, explain why the efcient outcome cannot be achieved