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1. Bargaining. It is November Ist, and Angus and Bronwen are arguing over how to divide the remainder of their left-over trick or treat candy. They decide on the following rules. On Nov 1st, Angus will make Bronwen an offer [sA(1), SB(1)] where sA (1) + SB (1) = 1. If Bronwen accepts then Angus gets a share s(1) of the candy and Bronwen gets SB (1). If Bronwen refuses, however, then no-one gets any candy on Nov Ist. In this case, on Nov 2nd, Bronwen gets to make Angus an offer [sA (2), SB(2)] where sA (2) + SB (2) = 1. If Angus accepts then Angus gets a share sA(2) of the candy and Bronwen gets SB (2). If Angus refuses, however, then no-one gets any candy on Nov 2nd. In this case, on Nov 3rd, Angus gets to make Bronwen an offer [SA (3), SB(3)] where sA (3) + SB (3) = 1. If Bronwen accepts then Angus gets a share sA(3) of the candy and Bronwen gets sB (3). If Bronwen refuses, however, then no-one gets any candy on Nov 3rd. In this case, on Nov 4th, Bronwen gets to make Angus an offer [sA (4), SB (4)] where sA (4) + SB (4) = 1. If Angus accepts then Angus gets a share sA(4) of the candy and Bronwen gets SB (4). If Angus refuses, however, then all the candy is thrown away by their parents. There is a catch. Both Angus and Bronwen are hungry and impatient for candy so they discount candy tomorrow. For Angus, each day, one candy tomorrow is worth only A candy today where 6A