8. Kate and Steve are bargaining over how to divide $3,960. Kate is more patient than Steve. Kate's discount factor is 0.75 and Steve's is 0.5. They agree to play a three- stage bargaining game. In the first stage, Kate proposes a division of the $3,960 and Steve decides whether to accept or reject the proposal. If he accepts, the game ends. If Steve rejects, he then suggests a division. If Kate accepts Steve's suggestion, the game ends, otherwise Kate makes a third proposal, which Steve may choose to accept. If Steve rejects this last proposal, both get nothing. a) Represent this game in extensive form and write down the unique subgame perfect Nash Equilibrium of the game. What are the equilibrium payoffs? b) In a new version of the game, the first two stages of the game are as in part a). However, if the game reaches the third stage, it is Steve who makes a second offer and the game ends after this offer. How does this change the equilibrium payoffs? Which version of the game does Steve prefer? c) In a third version of the game, there is no limit to the number of stages. That is, they agree to alternate offers potentially infinitely. What are the payoffs in the subgame perfect Nash Equilibrium