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Rodney and John are trying to split 100. In bargaining round 1, R makes an offer at cost 0, proposing to keep S1 for himself and John either accepts (ending the game) or rejects. In round 2, John offers to give S2 to Rodney, the offer costs John c. R either accepts or rejects. In round 3 R makes an offer of S3 at cost c and John either accepts or rejects. IF no offer is accepted, the 100 is gone to the third player Talyor.
a) Draw this strategic situation in a game tree.
b) Calculate the equilibrium outcome for c=0, c=80 and c=10
c) what happens if c=0,but John is very emotional and would with a chance of 50% spit in R's face and throw the 100 to taylor if Rodney ptopodrd S=100? Assume that Rodney knows John's personality perfectly.
now Talyor and John shipwrecked on a desert planet, are trying to split 100 kg of bread (B) AND 100 littres of cola (C), their only supplies. T's utility function is Ur=B+0.5C and John's is Uj=3.5B+3.5C. If they cannot agree, they fight to the death, with U=0 for the loser. John wins with a probability of 0.8
e) what is the threat point
f) with a 50-50 split of the supplies, what are the utilities if the two players do not renegotiate? is this efficient?
g) draw the threat point and the Pareto frontier in utility space (Ur on the horizontal axis)
h) accoording to the Nash bargaining solution , what are the utilites? how are the goods split?
i) suppose T discovers a cookbook full of recipes for a variety of cola candies and bread muffins and his uility function becomes UR=10B+5c show that the split of goods in part h) remains the same despite his improved utility function.
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