Question
Consider the three-person game where values of coalitions are defined as follows: v{} = 0; v{1} = v{2} = v{3} = 0; v{1,2} = 100;
Consider the three-person game where values of coalitions are defined as follows:
v{} = 0; v{1} = v{2} = v{3} = 0; v{1,2} = 100; v{1,3} = 150; v{2,3}= 300; v{1,2,3}= 1000:
(a) Find the Shapley values of the players.
(b) Find the core of the game (it may be empty). If the core is empty, what does it mean?
Step by Step Solution
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a The Shapley values of a player are the expected values of a players contributions to all coalitions that can be formed We can calculate the Shapley values of the players by using the formula i 1n S vS i vS n S 1 S where n is the number of players 3 in this case S is a coalition ...
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Numerical Analysis
Authors: Richard L. Burden, J. Douglas Faires
9th edition
538733519, 978-1133169338, 1133169333, 978-0538733519
