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Dummies. We defined a dummy as a player that is never critical. Explain why each of the
Chapter 2, Problem 61(choose chapter or problem)
Dummies. We defined a dummy as a player that is never critical. Explain why each of the following is true: (a) If P is a dummy, then any winning coalition that contains P would also be a winning coalition without P. (b) P is a dummy if and only if the Banzhaf power index of P is 0. (c) P is a dummy if and only if the Shapley-Shubik power index of P is 0.
Questions & Answers
QUESTION:
Dummies. We defined a dummy as a player that is never critical. Explain why each of the following is true: (a) If P is a dummy, then any winning coalition that contains P would also be a winning coalition without P. (b) P is a dummy if and only if the Banzhaf power index of P is 0. (c) P is a dummy if and only if the Shapley-Shubik power index of P is 0.
ANSWER:Step 1 of 3
a)
Suppose there is a winning coalition that contains , is also a winning coalition without . That means is never a critical player in that coalition which means is a dummy