Question 1: Consider a public goods game with 20 players. Each player receives an initial endowment of $10. Each player's final payoff is given by: - I = (E = x;) + 0.25 * Xi where E is the initial endowment, x; is the player's individual contribution, and ; x; is the sum of all players' contributions. a) Derive the individual contribution which maximizes each player's individual payoff. b) Derive the individual contributions which maximizes the sum of all players' payoffs. c) Based on Elinor Ostrom's article, what are some ways in which one can increase the amount of cooperation in a public goods game?