Question 1 Two players bargain over a pie of size 1. There are two rounds. In the first round, both players simultaneously propose an offer/demand. If the proposals are consistent with each other (i.e., the sum of demands is no larger than 1), they split the pie accordingly. Otherwise, they continue to the next round, and the size of the pie shrinks to 0.7. In the second round, player 1 proposes a division, and player 2 decides either to accept or reject it; If the proposal is rejected, the game ends and both get 0; if the proposal is accepted, the pie is allocated accordingly. Consider the concept of subgame perfect equilibria. 1. In the second round, what will be the equilibrium outcome? 2. Can there be a subgame perfect equilibrium such that an agreement is reached in the first round with a division (0.8, 0.2), i.e., 0.8 to player 1 and 0.2 to player 2? 3. Can there be a subgame perfect equilibrium such that, in the first round, an agreement is reached with the division (0.6, 0.4)? 4. Can there be a subgame perfect equilibrium in which there is a disagreement in the first round