Consider a game with two players. One of them (call player 1, proposer) is given specific amount of money (say, $10) and is told that the money should be split between players. Proposer must make an offer to the other player, which can be anything, ranging from 0 to the whole amount $10 and the rest proposer keeps for himself/herself. The other player (call player 2) is given nothing and whatever is given by the player 1 (proposer) is to be accepted by player 2. Even if the amount is unsatisfactory, player 2 cannot punish the player 1. If individuals are acting solely out of self-interest, what should be the amount that player 1 allocates to player 2?

Now consider the following change in the above described situation: once player 1 (proposer) communicates the decision/offer, player 2 (responder) can respond, by accepting it or rejecting it. If the responder accepts the money is split per the proposal, but if responder rejects, both players are getting nothing. They both know about the consequences of the accepting and rejecting the offer. This is a sequential move game and the proposer is the first mover (was given $10). Assume the proposer has just two strategies: propose a fair split (50/50) or unfair split (70/30). Draw the game tree and find subgame perfect Nash equilibrium of this game (apply backward induction). Show the steps of your solution and in case of explanations keep them short and to the point.