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The basketball team at a small high school consists of 3 seniors, 3 juniors and a coach. In what follows, I use the word "players" to mean players in the game theory model, including both basketball players and the coach. To choose the team captain, these are the winning coalitions: 1) 3 Seniors is winning without any other players. 2) Any group of 4 players including at least 2 seniors is winning. 3) Any group of 5 players or more players is winning. Determine the Shapley values of the seniors, juniors, and the coach.

The basketball team at a small high school consists of 3 seniors, 3 juniors and a coach. In what follows, I use the word "players" to mean players in the game theory model, including both basketball players and the coach. To choose the team captain, these are the winning coalitions: 1) 3 Seniors is winning without any other players. 2) Any group of 4 players including at least 2 seniors is winning. 3) Any group of 5 players or more players is winning. Determine the Shapley values of the seniors, juniors, and the coach.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The basketball team at a small high school consists of 3 seniors, 3 juniors and a coach. In what follows, I use the word "players" to mean players in the game theory model, including both basketball players and the coach. To choose the team captain, these are the winning coalitions: 1) 3 Seniors is winning without any other players. 2) Any group of 4 players including at least 2 seniors is winning. 3) Any group of 5 players or more players is winning. Determine the Shapley values of the seniors, juniors, and the coach.
Transcribed Image Text:The basketball team at a small high school consists of 3 seniors, 3 juniors and a coach. In what follows, I use the word "players" to mean players in the game theory model, including both basketball players and the coach. To choose the team captain, these are the winning coalitions: 1) 3 Seniors is winning without any other players. 2) Any group of 4 players including at least 2 seniors is winning. 3) Any group of 5 players or more players is winning. Determine the Shapley values of the seniors, juniors, and the coach.
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