Players 1 and 2 are bargaining over how to split a prize of size 100. In time period 1, player 1 proposes a share of the prize x to player 2 and player 2 may accept or reject his offer. If he accepts, the game ends with the proposed distribution by player 1 i.e., payoffs (100-x, x). If player 2 rejects, the game moves to the second time period, in which the size of the prize becomes half due to some external punishment. In the second time period, player 2 proposes a share y to player 1 and player 1 can either accept, resulting in payoffs y to player 1 and the remainder to player 2. In case player 1 rejects then the game moves to round 3. In round 3, the prize shrinks to 1/4th of the original size and each player gets the prize randomly with a probability of half by flipping a coin and the game finishes.

Solve for a subgame perfect equilibrium to this game.