Abby, Ben, and Clara are members of a three-person society that is considering a public investment, something that the entire society will enjoy. In order to move ahead with the investment, each person must decide whether they will contribute to the investment or not. Suppose that each person has $100 and must decide whether to contribute it or not without knowing others' choices.  Any money contributed goes into a fund where its value is multiplied by 2 and then split evenly among the members of society.  Any money not contributed is kept by the individual not contributing it. 

a. Suppose that Abby, Ben, and Clara play the game described above once. Formulate a normal-form representation of the game described above. A complete normal-form representation will clearly and accurately identify players, strategies, and payoffs.

b. Find all of the pure strategy Nash equilibria of the game you modeled in part a. above.

c. Does this game have any mixed strategy Nash equilibria? If yes, explain why. If not, explain why not