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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 This is what I got from the expert Can you explain where are 31 and 30 come from

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 This is what I got from the expert Can you explain where are 31 and 30 come from

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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  • 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

This is what I got from the expert

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.
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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