Five people have the opportunity to make a non-refundable contribution of $1000 toward a public good (denoted by C), or not (denoted by N ). So each player's strategy set is {C, N }. The good is provided if and only if 3 or more people contribute; that is, the good is provided if and only if at least $3000 is collected. For any player, the best outcome is that the good is provided and the player does not contribute; the second best outcome is that the good is provided and the player contributes; the third best outcome is that the good is not provided and the player does not contribute; the worst outcome is that the good is not provided and the player contributes. (a) Let M be the number of people other than the representative player who choose to contribute (C). Construct a payoff function for a repre- sentative player, and identify the representative player's best response function by underlining payoffs. (b) Indicate whether each of the following strategy combinations is or is not a Nash equilibrium, and using the best response function in Part a), explain why it is or is not an equilibrium. (N,N,N,N,N), (C,C,C,C,C), (N,C,C,C,C), (N,N,C,C,C), (N,N,N,C,C), (N,N,N,N,C) (c) Now look at the strategy combination or combinations in Part b) that are Nash equilibria, and indicate whether they are or are not Pareto- optimal. (d) Find all the Nash equilibrium strategy combinations