Two players are to divide $2,000 between them. The utility functions of the players are the amounts of money they receive: u1(x) = u2(x) = x. If they cannot come to agreement, neither of them receives anything.
For the following cases, describe the bargaining game derived from the given situation, in utility units, and find its Nash solution of the game.
(a) Given any division which the players agree upon, the first player receives his full share under the agreed division, and the second player pays a tax of 40%.
(b) Repeat the situation in the previous item, but assume that the second player pays a tax of 60%.
(c) The first player pays a tax of 20%, and the second pays a tax of 30%.