Let ‘x' be the amount that player A asks for, and let ‘y' be the amount that B asks for, when making the first offer in an alternating-offers bargaining game with impatience. Their rates of impatience are ‘r' and ‘s' respectively.
a) If we use the approximate formula "x=s/(r+s)" for ‘x' and "y=r/(r+s)" for ‘y', and if B is twice as impatient as A, thenm A gets two-thirds of the surplus and B gets one-third. Verify that this result is correct.
b) Let ‘r'=0.01 and ‘s'=0.02, and compare the ‘x' and ‘y' values using the approximation method with the more exact solutions for ‘x' and ‘y' found by using the formulas "x=(s+rs)/(r+s+rs)" and "y=(r+rs)/(r+s+rs).