$(1)(5$ points$)$ A corporate board for a large company is made up of five members: Jane, Tom,

Sally, Emily, and Jason. Each member has a strict hierarchy: Jane is senior to Tom, Tom is

senior to Sally, Sally is senior to Emily, Emily is senior to Jason. The board must decide how

to split a $5,000,300$ dollar bonus among the five members of the board. The rules of board

are as follows.

The most senior member proposes a distribution among the members. After

observing the proposal, the five board members vote on whether to accept the

proposal or reject it$.$ If the proposal is rejected, then the most senior member is

fired and no longer participates in the process. In the case of a tie, the proposer's

vote decides whether to accept or reject. If a proposal is rejected, then the next

most senior member now proposes a distribution. If the proposal is accepted, then

the distribution is received by the members of the board.

Each board member cares about three main factors. $(1)$ They do not want to be

fired $(2)$ If they are not fired, then they want to get the most dollars they possibly

can. $(3)$ Each board member would prefer to fire a board member, if all other results

would otherwise be equal.

Finally the board members do not trust each other and will not follow any promises

except for the proposal. $($Assume that any offer must be in whole dollars $0,1,2,$dots. $)$

Find the Nash equilibrium for this game.