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Divide-the-Dollar Game. Three players will be given a dollar if they can decide, by majority vote, how to divide the dollar among themselves. Here we take N = {1,2,3} and the characteristic function as v(p) = v(1) = v(2) = v(3) = 0; v(1, 2) = v(1, 3) = v(2, 3) = v(1, 2, 3) = 1. Let 0 ≤ a < / and K₁,0 be the set of all imputations in which Player 1 gets a. Show that K₁, is an N-M solution of the Divide-the-Dollar Game. Can you find another N-M solution of the Divide-the-Dollar Game ?

Divide-the-Dollar Game. Three players will be given a dollar if they can decide, by majority vote, how to divide the dollar among themselves. Here we take N = {1,2,3} and the characteristic function as v(p) = v(1) = v(2) = v(3) = 0; v(1, 2) = v(1, 3) = v(2, 3) = v(1, 2, 3) = 1. Let 0 ≤ a < / and K₁,0 be the set of all imputations in which Player 1 gets a. Show that K₁, is an N-M solution of the Divide-the-Dollar Game. Can you find another N-M solution of the Divide-the-Dollar Game ?

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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Divide-the-Dollar Game. Three players will be given a dollar if they can decide, by majority vote, how to divide the dollar among themselves. Here we take N = {1,2,3} and the characteristic function as v(p) = v(1) = v(2) = v(3) = 0; v(1, 2) = v(1,3) = v(2, 3) = v(1, 2, 3) = 1. Let 0 ≤ a < and K₁, be the set of all imputations in which Player 1 gets a. Show that K₁, is an N-M solution of the Divide-the-Dollar Game. Can you find another N-M solution of the Divide-the-Dollar Game ?
Transcribed Image Text:Divide-the-Dollar Game. Three players will be given a dollar if they can decide, by majority vote, how to divide the dollar among themselves. Here we take N = {1,2,3} and the characteristic function as v(p) = v(1) = v(2) = v(3) = 0; v(1, 2) = v(1,3) = v(2, 3) = v(1, 2, 3) = 1. Let 0 ≤ a < and K₁, be the set of all imputations in which Player 1 gets a. Show that K₁, is an N-M solution of the Divide-the-Dollar Game. Can you find another N-M solution of the Divide-the-Dollar Game ?
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