Two players are put in separate rooms. Each player is given $10. The player can use this money in either of two ways. He can keep it or he can contribute it to a public fund. Money that goes into the public fund gets multiplied by 1.6 and then divided equally between the two players. If both contribute their $10, then each gets back $20 x 1.6/2 = $16. If one contributes and the other does not, each gets back $10 x 1.6/2 = $8 from the public fund so that the contributor has $8 at the end of the game and the noncontributor has $18-his original $10 plus $8 back from the public fund. If neither contributes, both have their original $10.c) Suppose that exactly K of the other players contribute. If you keep your $10, you will have $10 plus your share of the public fund contributed by others. What will your payoff be in this case? If you contribute your $10, what will be the total number of contributors? What will be your payoff? d) If B=3 and N=5, what is the dominant strategy equilibrium for this game? Explain. e) In general, what relationship between B and N must hold for Keep to be a dominant strategy?h) Sometimes the action that maximizes a player's absolute payoff, does not maximize his relative payoff. Consider the example of a voluntary public goods game as described in Question 2 in Assignment 5, where now we have B=6 and N=5. Suppose that four of the five players contribute their $10, while the fifth player keeps his $10. What is the payoff of each of the four contributors? What is the payoff of the player who keeps his $10? Who has the highest payoff in the group? What would be the payoff to the fifth player if instead of keeping his $10, he contributes, so that all five players contribute. If the other four player contribute, what should the fifth player do to maximize his absolute payoff? What should he do to maximize his payoff relative to that of the other players? i) If B=6 and N=5, what is the dominant strategy equilibrium for this game? The payoff matrix of this game is:

		Player B
		Contribute	Keep
Player A	Contribute	$16,$16	$8,$18
	Keep	$18,$8	$10,$10