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Game Theory: An Introduction, 2nd Edition by E. N. Barron

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Problems

6.25 There are three types of planes (1, 2, and 3) that use an airport runway. Plane 1 needs a 100-yard runway, 2 needs a 150-yard runway, and 3 needs a 400-yard runway. The cost of maintaining a runway is equal to its length. Suppose this airport has one 400-yard runway used by all three types of planes and assume also that only one plane of each type will land at the airport on a given day. We want to know how much of the $400 cost should be allocated to each plane.

(a) Find the characteristic function.
(b) Find the least core and show it has only one allocation.

6.26 In a glove game with three players, player 1 can supply one left glove and players 2 and 3 can supply one right glove each. The value of a coalition is the number of paired gloves in the coalition.

(a) Find the characteristic function.
(b) Find C(0).

6.27 Consider the normalized characteristic function for a three-person game:

Unnumbered Display Equation

Find the core, the least core X1, and the next least core X2. X2 will be the nucleolus.

6.28 Find the fair allocation in the nucleolus for the three-person characteristic function game with

Unnumbered Display Equation

6.29 In Problem 6.12, we considered the problem in which companies can often get a better cash return if they invest larger amounts. There are three companies who may cooperate to invest money ...

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