Consider a situation where the level of a public good is determined by the contributions of two individuals. Each agent begins with an endowment of 10 units of the private good (that is, (1 = 10 and (2 = 10) and has a utility function: U.(G, Xi) = 2G1/2 + Xi where gi is agent i's contribution to the public good, and G = gi + g2. As in other versions of this model we have considered, whatever agent i does not contribute to the public good, agent i consumes privately (that is, Xi = ai - gi). Assume that an individual's contribution can take on one of three levels: gi = {0,2,4) . These three levels are the only possible contributions. 1 Taking the payoffs as each player's utility, draw out the simultaneous move version of this game. 2 Identify any pure strategy Nash equilibria of this game. 3 For a social planner that values each agent's utility equally highly, what is the optimal level of G? (the social planner's choice of G is limited by the same restriction on the individual contribution levels in the previous parts)