Suppose that there are 100 legislators in a bargaining situation, splitting a pie of size 1. Player 1 proposes a split between the 100 players, including himself (in any continuous amount, he can allocate different shares to different players as long as these shares add up to 1). The other 99 players then vote on whether to split the pie in that way or not. If a majority of them (that is 50) vote for the split,then the split is implemented, each player obtaining the proposed share. If a majority vote against the split, then each player obtains 1 percent of the pie.

a) What is a subgame-perfect Nash equilibrium proposal of player 1, and what is the resulting outcome of the game?

b) Suppose now that different players obtain different shares (adding up to 1) when the majority vote is not passed. What happens in a SPNE then? (You can describe the solution to this in words, if that is easier).