Let's examine a more general version of the voluntary public goods game described in the previous problem. This game has N players, each of whom can give 10 euros or nothing to the public fund. All the money that is given to the public fund is multiplied by a number B> 1 and then it is distributed equally among all the players who participate in the game (including those who do not give their money). Therefore, if all the N players give 10 euros to the fund, the amount that is to be distributed among the N players is equal to 10 euros BN and each receives 10 euros BN / N = 10 euros B from the public fund.

(a)If B> 1, in which of the following cases does each player get the highest score? a) All players give their 10 euros or b) all players keep their 10 euros.

(b)Suppose they give up their money exactly K of the other players. If you keep your 10 euros, you will have these 10 euros plus your share of the public fund to which others have contributed. What result will you get in this case? If you give your 10 euros, how many people in total will give their money? What result will you get?

(c)If B = 3 and N = 5, what is the dominant strategy equilibrium of this game? Explain your answer.

(d)In general, what relationship must there be between B and N for "keeping the money" to be a dominant strategy?

(e)Sometimes the decision that maximizes a player's absolute outcome does not maximize his relative outcome. Consider the example of a voluntary public goods game that we described earlier, in which B = 6 and N = 5. Suppose that four of the five players in the group give up their 10 euros, while the fifth keeps his. What result does each of the players who give up their money get? What result does the one who keeps his 10 euros get? Who gets the best result in the group? What result would the fifth player get if instead of keeping his 10 euros, he handed it over, so that all five would give up their money? If the other four players turn over their money, what should the fifth player do to maximize his outright score? What should you do to maximize your score relative to the other players?

(f)If B = 6 and N = 5, what is the dominant strategy equilibrium in this game? Explain your answer.