A legislature with three members has $1 to allocate for "pork barrel" projects to the legislators' districts. The legislature works as follows: First, a proposer is selected at random; each legislator has an equal chance to be the proposer. Next the proposer proposes a share of the dollar for each of the three legislators. Shares can be any number from 0 to 1, including 0 and 1 (i.e., the shares are percentages of the pie), and the sum of the shares cannot exceed 1. Then the legislature takes a majority vote on the proposal. If it wins a majority of votes (2 or 3), the legislators are all paid their proposed shares. If it does not win a majority, a status quo policy remains in force, in which legislator 1 receives $.30, legislator 2 receives $.35, and legislator 3 receives $.10. A legislator's payoff is the share of the pie s/he receives and all wish to maximize their own payoff. Assume that when players vote, they vote in favor of the proposal if they obtain equal payoffs whether it passes or fails.

(a) Suppose legislator 1 is selected as the proposer. What are the shares each player obtains in the subgame perfect equilibrium?

(b) Suppose legislator 2 is selected as the proposer. What are the shares each player obtains in the subgame perfect equilibrium?

(c) Suppose legislator 3 is selected as the proposer. What are the shares each player obtains in the subgame perfect equilibrium?