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1.2 A Better Understanding of the Need f... > 1.2 A Better Understanding of the Ne... - Pg. 5

1.2 A Better Understanding of the Need for Game Theory 5 FIGURE 1.1 A physical interpretation (Aumann, 1985) of the game theoretical solution to the bankruptcy problem solved in Aumann and Maschler (1985). for the cases where it is worth 200 and 300 are very surprising and have baffled many scholars for two thousands years. How can this "mystery" be explained? Many unsatisfy- ing answers were given to this problem, but only in 1985 was a relevant answer derived. It was given by game theorists (namely by Aumann and Maschler (1985)) who proved that this bankruptcy problem can be formulated as a cooperative game for which each solution reported in Table 1.1 corresponds to the nucleolus of the game. We will not go into the details of cooperative games here (see Aumann and Maschler (1985) for more details) but,