Explanation The method of markers is a discrete fair-division method. In this method, start with items lined up in a random but fixed sequence called an array. Each of the player make an independent bid on the items in the array. The bid consists of dividing the array into segments of consecutive items (as many segments as there are players) so that each of the segments represents a fair share on the entire set of items. After considering the bids of a respective player, remove its markers Given: Quintin, Ramon, Stephone, and Tim are dividing a collection of 18 classic superhero comic books using the method of markers. The comic books are randomly lined up in the array shown below. (The W’s are Wonder Woman comic books, The S’s are spider-Man comic books, the G’s are Green Lantern comic books, and the B’s are Batman comic books.) W S S G S W W B G G G S G S G S B B The value of the comic books in the eyes of each player is shown in the following table; Quinton Ramon Stephone Tim Each W is worth $ 12 $ 9 $ 8 $ 5 Each S is worth $ 7 $ 5 $ 7 $ 4 Each G is worth $ 4 $ 5 $ 6 $ 4 Each B is worth $ 6 $ 11 $ 14 $ 7 Calculation: Each player divides the array into segments such that each segment has equal value(approximately). The value of the items for each player is given by, Quinton Ramon Stephone Tim Each W is worth $ 12 $ 9 $ 8 $ 5 Each S is worth $ 7 $ 5 $ 7 $ 4 Each G is worth $ 4 $ 5 $ 6 $ 4 Each B is worth $ 6 $ 11 $ 14 $ 7 There are 3 W’s, 6 S’s, 6 G’s and 3 B’s in the array. The value of array for player Quinton is, 3 ( $ 12 ) + 6 ( $ 7 ) + 6 ( $ 4 ) + 3 ( $ 6 ) = $ 120 To determine b. The allocation of comic books to each player and the comic books that are left over.

Excursions in Modern Mathematics (9th Edition)

9th Edition

ISBN: 9780134468372

Author: Peter Tannenbaum

Publisher: PEARSON

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Chapter 3, Problem 57E

To determine

1.

To explain:

The placement of each player’s markers.

To determine

b.

The allocation of comic books to each player and the comic books that are left over.

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Chapter 3, Problem 56E

Chapter 3, Problem 58E

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1. To explain: The placement of each player’s markers.

Solution Summary: The author explains the method of markers, which is a discrete fair-division method. Each player makes an independent bid on the items in the array.