Consider a the following two$-$player game where an amount of $10$$ is to be split among the

two players. Player $1,$ called $$proposer$,$ makes a take$-$it$-$or$-$leave$-$it offer to player $2,$ called

$$responder$.$ Suppose that the proposer can propose one of two splits: $($x$1,$ x$2)=(9,1)$

$($uneven split$)$ or $($x$1,$ x$2)=(5,5)($even split$).$ After observing the proposal, the responder

can either accept or reject the offer. If he accepts, the proposal is implemented and the

money is split accordingly. If the offer is rejected, no player receives anything resulting in

a payoff of $(0,0).$ Suppose that the only thing that the players care about is the monetary

payoff.

$($a$)$ Write down the normal form of this game. How many strategies does each player

have? Find all NE of the game.

$($b$)$ Draw the game tree and find all SPNE of the game.

$($c$)$ Use the answers to $($a$)$ and $($b$)$ to explain the concept of a credible threat.