Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
  • Shapley value of each senior = (31 + 3(1/2 + 1/2 + 1))/5040 = 37/840
  • Shapley value of each junior = (3*(1/6 + 1/6 + 0) + 3*0)/5040 = 1/840
  • Shapley value of the coach = (30 + 3(1/2 + 1/3) + 1*(1/3))/5040 = 19/840

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Can you explain where are 31 and 30 come from

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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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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