Consider the Rubinstein bargaining model of dividing $1 between A and B. A makes the first offer. If B accepts the offer then game ends. If B rejects the offer then B makes an offer to A in the next day. Suppose the bargaining game lasts for 4 days. If the final offer is rejected by A on day 4, they both go home with nothing. Assume A discounts future payoffs at rate α per day, and B discounts future payoffs at rate β per day. Solve the sub game perfect equilibrium payoffs to each player.