Game Theory. Please show all your work on paper preffered. Thank you. I will Upvote.

Consider the following two$-$player, $4-$period bargaining game with the common discount factor in $(0,1).$ The players are bargaining over surplus of $1.$ In this

game, if an offer is rejected in period $1,2$ or $3,$ then game moves to the next period.

If the offer is rejected in period $4,$ the game ends and both players receive $0.$ Player

$1$ makes offers in period $1$ and $4,$ and player $2$ makes offers in period $2$ and $3.$ Using

backward induction, find SPNE $($in pure strategies$)$ of this game. Find the equilibrium

payoffs of each player