Consider a Public Goods game with n>2 risk neutral players, each with an initial monetary endowment of 20. The players simultaneously choose how much to contribute to a public good. For each unit contributed, there is a return , with 1/ < < 1. The public good is distributed in full to each of the players. That is, if the total contributions are , each of the players gets back . a.

Derive the Nash Equilibrium of this game as well as the Pareto Optimal solution. (2 marks)

b. Assume the players are characterised by Fehr and Schmidt preferences with parameters and capturing the envy and advantageous inequity aversion respectively. What does the inequality < imply? (3 marks)

c. If there are n players each with an endowment of 20 who make contributions 1, 2, . . , , write down the utility of a player who contributes . (5 marks)

d. Is player better off contributing 0 or 20? (hint: assume players are contributing 0 and are contributing 20). (7 marks)